The 33-year-old Ireland international has put pen to paper on a two-year contract at Villa Park, bringing to an end his nine-year association with the Premier League side.
“I have enjoyed happy times at Stoke City but now is the time for a new football adventure — and what a club to join in Aston Villa,” Whelan said.
“We may be in the Championship but everything about this club screams Premier League — and it’s the job of the players to get us back up there.
“I am looking forward to working with Steve Bruce. I know he has a phenomenal record in achieving promotion to the top flight and, having spoken to him at length, I am more than aware of how much he wants to get back there again with this great club.”
Villa have paid Stoke an initial £1.25m (€1.4m) but the fee could rise to £2m (€2.2m) with certain add-ons and clauses.
Whelan made more than 330 appearances for Stoke after joining the club from Sheffield Wednesday for £500,000 (€558,000) in January 2008.
He helped the Potters clinch promotion to the Premier League during the 2008/09 season and was a mainstay in the team as Stoke went on to establish themselves in the top flight.
Whelan is the fourth new arrival at Villa this summer after the signings of Ahmed Elmohamady, John Terry and Sam Johnstone.
In other transfer news, West Ham have agreed a deal with Bayer Leverkusen to sign Mexico striker Javier Hernandez.
The Hammers have confirmed Hernandez, 29, will arrive in London in the next few days to finalise personal terms and undergo a medical.
Hernandez, Mexico’s all-time leading scorer, is set to become manager Slaven Bilic’s third summer signing after full-back Pablo Zabaleta and goalkeeper Joe Hart. The fee is believed to be around £13m (€14.5m).
Hernandez is a proven Premier League performer, having scored 59 goals during a four-year spell with Manchester United.
The player, known as ‘Chicharito’, then moved to Real Madrid on loan in 2014 and a year later signed for Leverkusen, where he scored 28 Bundesliga goals in 54 appearances.
Assuming the move goes through as planned, Hernendez could make his West Ham debut against former club United at Old Trafford on August 13.
Elsewhere, Monaco are threatening to report “important” European clubs to Fifa for making contact with star striker Kylian Mbappe without the club’s consent.
Mbappe is one of football’s hottest properties and a host of sides have been linked with a move for the 18-year-old France international, who scored 26 goals in all competitions as Monaco won Ligue 1 last season.
The French outfit have not named which clubs they believe have approached Mbappe — who has reportedly attracted offers of £100m (€111.6m) this summer — but have said they may turn to both the French Football League (LFP) and Fifa to take action against the offenders.
A club statement read: “AS Monaco state with regret that “important” European football clubs have made contacts with Kylian Mbappe (and his entourage) without authorisation from the club.
“AS Monaco want to remind these clubs that such actions are contrary to article 211 of the administrative regulation of the French Football League and to article 18.3 of Fifa’s regulation of the status and the transfer of players.
“To put an end to this unacceptable situation, AS Monaco are planning on asking the French Football League and Fifa to start disciplinary procedures against the offending clubs.”