The 28-year-old has signed a four-year contract at Portman Road, becoming Ipswich's 12th signing of the summer as Gary O'Neil continues to strengthen his squad following promotion. Flemming scored 11 league goals for Burnley last season despite the club's relegation from the Premier League, and has already added three more in his first four appearances of the new campaign.
O'Neil said he had been tracking the Dutchman's progress closely.
"He has good quality and experience and has started the new season well, so is a great addition to the group as we strengthen the squad further," the Ipswich boss said.
Burnley had hoped to keep hold of Flemming, who arrived from Millwall for £7million in 2025. Manager Nicky Hayen publicly urged the forward to stay after his side's win over West Ham in August, but Ipswich's interest ultimately proved decisive as the transfer window drew to a close.
Flemming, who began his career at Ajax before spells at PEC Zwolle, NEC Nijmegen and Fortuna Sittard, said he was relishing the chance to remain in the Premier League after enjoying his first taste of the top flight last season.
"I played in the Premier League last season and really enjoyed my first season at the top level, competing against the best players and teams in the world, so I am delighted to now be back in there with a great club like Ipswich," he said.
The move gives Ipswich Town fresh attacking options after a mixed start to their own return to the Premier League. O'Neil's side beat Sunderland 2-1 in their opening fixture before being thrashed 5-2 by Manchester United, and Flemming will hope to add firepower to a Tractor Boys attack looking to establish itself among the division's top flight after promotion.
Flemming's arrival caps a significant summer of spending at Portman Road as Ipswich look to avoid an immediate return to the Championship.
His departure leaves a considerable gap in Burnley's own attack, with Hayen having already signalled the club would look to bring in a replacement if the sale went through, and his versatility to play across the front line gives O'Neil another option as he shapes his side for the challenges ahead.