The 20-year-old spent the first half of last season on loan at Coventry City, scoring four times in 16 League One appearances for the Sky Blues.
Agyei also made three Premier League appearances from the bench for the Clarets last season, but has been allowed to move after the summer arrivals of Chris Wood, Jon Walters and Nahki Wells pushed him further down the pecking order.
Saddlers boss Jon Whitney told the official club website: "He's somebody we've been tracking over the summer. He's really highly thought of at Burnley and he made his Premier League debut against Liverpool at Anfield last season.
"He went out to Coventry last season and impressed there. He's been highly sought after by several clubs but we have got the deal done.
"He's a really good addition and he'll strengthen the squad. He's got raw pace and power and he's got goals in him as well. We're really pleased to get Daniel on board."
Agyei becomes the League One club's eighth signing of the summer transfer window.