No fee was officially disclosed on Tuesday (Wednesday AEST), but media reports say it is worth 117 million pounds ($A224 million), which surpasses England teammate Elliot Anderson's 116 million pounds ($A222 million) switch from Nottingham Forest to Manchester City earlier this month.
The all-time record Premier League transfer is still Sweden striker Alexander Isak's 125 million pounds ($A239 million) move from Newcastle United to Liverpool last year.
The 23-year-old Rogers, established as one of the Premier League's top attacking talents, has signed a contract with the London club until 2033.
"I'm so excited," he told the club's website.
"For me, Chelsea are the biggest club in London and a club I've always admired since I was a kid.
"I'm really excited about the project with the new manager, the players we've got and where the club is heading. That's why I'm here and I can't wait to get started."
Rogers is the third major signing made in the off-season by new Chelsea manager Xabi Alonso, following wingbacks Marco Palestra and Geovany Quenda.
Rogers was in England's team beaten by Argentina in their World Cup semi-final.
He scored 21 goals in 85 Premier League appearances for Villa, and last season helped guide the club to a top-four finish and to the Europa League title.
Rogers joined Villa from Middlesbrough in February 2024 for a reported fee of eight million pounds ($A15 million).
He made his England debut in November 2024 and has now won 22 caps for his country.
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