Rogers had been heavily linked with a move to Arsenal, but Chelsea hijacked the move at the end of last week to bring the player to Stamford Bridge.
"I'm so excited," said Rogers. "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."
He arrives at Chelsea after featuring six times for England at the 2026 World Cup, with his impressive form at Villa earning a call-up to Thomas Tuchel's squad.
The midfielder made 125 appearances for Villa, registering 31 goals and 29 assists in a significant jump in quality from previous spells at Middlesbrough, Lincoln, Bournemouth and Blackpool.
He first emerged as part of a highly successful Manchester City youth academy side and links back up with former teammates Cole Palmer and Liam Delap at Stamford Bridge.
Rogers becomes Chelsea's marquee signing under new manager Xabi Alonso, surpassing the transfer record set earlier in the window after Elliot Anderson's move to Manchester City (£116m).
“I’ve had a few conversations with Xabi Alonso. It’s important for me to be here that I need to understand what the manager’s like, how he is, how he wants to operate," he said.
“It very much fits with the way I see the game, the way I want to play, to be me, be free, and express myself.
"Him being a part of that was a massive decision for me to be here."