Both sides were beaten on the opening weekend of the new campaign and will be looking to get their seasons up and running at the second time of asking.
The 2016-17 campaign has not quite gone to plan for West Ham so far, with the club making an inauspicious start to what was meant to be a glorious new era.
Fresh off the back of an impressive year that saw them finish just four points off the Champions League places and moving into a glamorous new stadium, hopes were high that West Ham could make the final step up to challenge England's elite.
A summer of being knocked back in search of a top-quality centre-forward may prove to be a sign of things to come, though, and once they finally did bring in attacking reinforcements in the form of club-record signing Andre Ayew, the optimism was short-lived.
The Ghana international was forced off after just 35 minutes of his side's season opener against Chelsea on Monday night, and he will now spend four months on the sidelines with a thigh injury, potentially keeping him out until 2017.
That capped off a miserable start to the Premier League campaign after Diego Costa - who arguably should have been sent off earlier in the match - scored an 89th-minute winner to rescue all three points for Chelsea and leave West Ham empty handed from the London derby.
Another late goal cost them in their Europa League clash on Thursday too, with Astra Giurgiu earning a 1-1 draw in the first leg of their qualifier in Romania after Mark Noble had given his side the lead.
The Hammers still have the slight advantage at the halfway stage of the tie courtesy of that away goal, but manager Slaven Bilic may not be able to rest as many players as he would have liked before next week's trip to Manchester City.
Their only previous competitive match at the Olympic Stadium saw them overturn a first-leg deficit to beat Domzale 3-0 in the previous qualifying round, though, so they will be confident of using their home advantage to their benefit once again to reach the group stages - ideally off the back of another home triumph this weekend.
West Ham lost just three times in front of their own fans last season as they bid farewell to the Boleyn Ground, and although clubs often struggle in the immediate aftermath of moving stadiums, Bilic will be hopeful that his side can hit the ground running in their new home.
Recent form: L
It is never ideal to be propping up the Premier League table, but if there is a time to do it then it is after matchday one, when you still have 37 games to rectify the situation.
That is the position Bournemouth find themselves in heading into this game having been the only team to lose by a two-goal margin on the opening weekend as Jose Mourinho's star-studded Manchester United side came to town.
The result will certainly not be enough to make Eddie Howe panic; United were always expected to win that match and Bournemouth were beaten by Aston Villa on the opening day of last season before going on to enjoy an impressive debut campaign in the top flight.
Indeed, they lost their opening two games of last season before finally picking up their first ever top-flight victory when visiting West Ham. It may be a different stadium this time around, but the occasion will still stir up fond memories for the Cherries.
If the historical significance of the result wasn't enough to do that, the spectacle itself was, with Callum Wilson scoring a hat-trick in a thrilling 4-3 victory that was the first step towards Bournemouth finishing 16th in the table, some five points clear of relegation.
Howe would surely be content with a similar finish this time around as they look to avoid the dreaded second-season syndrome, but if you include the tail end of last term then they have only picked up one point from their last six Premier League outings.
The Cherries actually amassed more points away from home than they did in front of their own fans last season, though, so an away trip to a ground which may not quite feel like home for West Ham yet could be exactly what they need to kick-start their campaign.
Recent form: L
West Ham have a number of injury concerns heading into this weekend's match, including playmaker Dimitri Payet, who is suffering from a knock.
The France international was given just 23 minutes off the bench in Monday's meeting with Chelsea, but he is expected to recover in time to start against Bournemouth.
Ayew has joined Aaron Cresswell as a long-term absentee, while Manuel Lanzini and new signing Sofiane Feghouli - one of just two players to have scored a competitive goal at West Ham's new home - will not return until after the international break.
Another new signing Havard Nordtveit is also doubtful along with Diafra Sakho, so Andy Carroll should lead the line once again while Jonathan Calleri, who made his debut in midweek, could drop to the bench.
The likes of Max Gradel, Lewis Grabban and Benik Afobe will all be hopeful of a recall, although the latter has scored just once in his last 12 appearances having begun his Bournemouth career with three goals in four games.
West Ham possible starting lineup:
Adrian; Antonio, Collins, Reid, Masuaku; Kouyate, Noble, Tore; Payet, Carroll, Valencia
Bournemouth possible starting lineup:
Boruc; Smith, Francis, S Cook, Daniels; L Cook, Surman, Arter; Ibe, Wilson, King
Head To Head
These two sides have only ever met seven times before in any competition, and the corresponding fixture last season was the first time that Bournemouth have beaten West Ham.
The Hammers had won all of their previous three home games against the Cherries, in 1929, 1990 and 1999, and average three goals per game from the four times they have hosted Bournemouth.
We say: West Ham 3-1 Bournemouth
The West Ham fans have taken well to the Olympic Stadium so far, and the first Premier League match at their new ground is likely to be a special occasion. Bournemouth can cause problems, as they proved last season, but the home advantage coupled with the potential return of Payet swings this one in West Ham's favour.