The 27-year-old has agreed terms on a five-year contract with the Premier League giants, which will officially start when the window opens for business.
Chelsea's transfer ban meant that they were unable to bring any new players to the club ahead of the 2019-20 campaign, but they have moved quickly to secure Ziyech on a long-term deal.
The Morocco international has spent the last four seasons with Ajax following a move from Twente and played a key role in the Dutch giants winning a league and cup double last term in addition to reaching the semi-finals of the Champions League.
Here, Sports Mole looks at how Ziyech and Chelsea's current wingers stack up against each other across the board during the 2019-20 season.
Ziyech has outscored Willian, Pedro, Callum Hudson-Odoi and Christian Pulisic during the 2019-20 campaign. Indeed, the Morocco international has managed eight goals in 35 appearances in all competitions; Willian has seven, Pedro two, Hudson-Odoi four and Pulisic six.
There is no question that goals from a wide area - and from the attack in general - has been a problem for Frank Lampard's side this season. Indeed, there has been a huge focus on Tammy Abraham to find the back of the net, and the England international has had his injury problems in recent weeks.
Ziyech has only scored six times in 21 league matches this season, which is hardly terrific, although he has contributed two Champions League goals in six group-stage appearances. Willian, on the other hand, has only scored one Champions League goal this term, while Pedro, Hudson-Odoi and Pulisic have just one between them.
Only one player in this article has scored a hat-trick at club level this season, with Pulisic scoring three times against Burnley towards the end of October. Both Willian and Ziyech have managed braces this term, but the lack of goals from Pedro and Hudson-Odoi has harmed the London club.
Interestingly, though, Ziyech has not actually scored for Ajax in any competition since the turn of the year; his last league goal was against ADO Den Haag on December 22, but both Willian and Pedro managed a goal and an assist each in Chelsea's 4-0 win over Everton earlier this month.
There is only one winner in this category with Ziyech's assist record during the 2019-20 campaign very, very impressive. Indeed, in 35 matches in all competitions, the Morocco international has contributed 21 assists.
Thirteen of those assists have come in the Eredivisie, but he also managed five assists in six Champions League appearances or eight in 10 if the qualification stage of the competition is counted.
Willian and Pulisic are next in line with six assists each in all competitions, but Pedro has only contributed three assists while Hudson-Odoi has five.
Lampard will certainly be hoping that Ziyech can bring some creativity to the team next season, and it is worth noting that the new arrival has managed an incredible 82 assists in 165 appearances for Ajax in all competitions since arriving in 2016, which is some rate.
What's more, Ziyech has five goals and eight assists in 17 Champions League appearances for his Dutch side overall, showing that he is more than capable of producing at the top level.
Ziyech has a pass success rate of 77.4% in the Eredivisie this season, while his Champions League pass success rate over six Champions League group appearances is 76%.
Hudson-Odoi actually has a pass completion rate of just over 85% in the Premier League this season, while Pedro's is just over 83%. Hudson-Odoi's touches (612) in the Premier League this term are also much higher than Pedro's (460), while the Englishman has created more big chances (5).
Pulisic's pass completion is around 80%, while Willian boasts 83% in the same category, showing that Hudson-Odoi, statistically, keeps hold of the ball the most on this list, but the Englishman's contribution in terms of goals and assists still needs a lot of work.
Pulisic's shooting accuracy is down at 58.6%, Willian's is 50%, Hudson-Odoi's is 40%, while Pedro's is 69.2%, which is perhaps a surprise considering the Spaniard's lack of goals this season.
As for Ziyech, he has averaged just over four shots per game in the Eredivisie this season, while he has provided 3.7 key passes per game and 2.6 dribbles per game in the same competition.
Pedro's defensive statistics in the Premier League this season are actually quite strong, boasting nine interceptions, 15 tackles and three aerial battles won. Hudson-Odoi, though, has not made a single block, while he has only managed three successful tackles in England's top flight this term.
As for Willian and Pulisic, the statistics heavily favour the former. Indeed, Willian has 20 interceptions, 39 tackles and seven clearances to his name in the Premier League this season. Pulisic, on the other hand, has made just three interceptions, 14 tackles and four clearances.
As a result, it is not too difficult to see that Willian has contributed the most defensively for Chelsea this season, especially in the Premier League. The Brazil international is entering the final stages of his contract at Stamford Bridge, though, and could leave on a free transfer this summer.
Ziyech, meanwhile, has a record of 1.8 tackles per game in the league this season but that number rises to 2.3 per game in the Champions League. The attacker, according to the statistics, has only produced an average of 0.5 interceptions per game in the league, though, while that number drops to 0.3 in the Champions League.
In truth, Ziyech is so important for Ajax in the final third that he is not expected to do too much going in the opposite direction. He has played a lot of football off the right this season but has also been used as an attacking midfielder, and it will be fascinating to see where Lampard decides to deploy the new arrival.