Bracken – who will win his 42nd cap – replaces Andy Gomarsall, who drops down to the replacements' bench.
This will be the 31-year-old's first England start for 10 months, the scrum-half wearing the No.9 shirt in England's final Six Nations tie against Italy last season and is his first game back since he was concussed while playing for his club against Gloucester on February 2.
England coach Clive Woodward had hinted earlier in the week that Northampton's Matt Dawson – a late withdrawal from the team to face France – would be fit to resume his place in the squad, but the scrum-half has failed to recover from a calf injury.
The other two changes to the starting line-up are in the forwards with Graham Rowntree and Lawrence Dallaglio replacing injury victims Jason Leonard and Lewis Moody.
Both Rowntree and Dallaglio featured strongly in England's 25-17 win over France last week after joining the action from the bench and the latter, in particular, would have made a strong case for inclusion in the starting line-up against Wales even if Moody had not been sidelined with a shoulder injury.
Dallaglio completes a vastly experienced back row, alongside fellow Lions Neil Back and Richard Hill, the trio boasting a mammoth 159 caps between them.
The changes to the starting XV mean that uncapped London Irish prop Mike Worsley and Wasps' back rower Joe Worsley are called up to the bench.
"If Dawson has been fit then he would have started. It is tough on Andy Gomarsall, but his form has not quite been their for his clubs, and Kyran just gets the nod," said Woodward at the team announcement.
"We are hoping that Jason Leonard will be fit to play another another part in the Championship this season. He has had a scan and he is very doubtful for the Italy game.
"Lewis Moody will see a specialist today, and he couldn't train today or tomorrow."
England: 15 Jason Robinson (Sharks), 14 Dan Luger (NEC Harlequins), 13 Will Greenwood (NEC Harlequins), 12 Charlie Hodgson (Sharks), 11 Ben Cohen (Northampton Saints), 10 Jonny Wilkinson (Newcastle Falcons), 9 Kyran Bracken (Saracens), 8 Richard Hill, 7 Neil Back (Leicester Tigers), 6 Lawrence Dallaglio, 5 Ben Kay (Leicester Tigers), 4 Martin Johnson (Leicester Tigers, captain), 3 Julian White (Bristol Shoguns), 2 Steve Thompson (Northampton Saints), 1 Graham Rowntree (Leicester Tigers).Replacements: 16 Mark Regan (Leeds Tykes), 17 Mike Worsley (London Irish), 18 Danny Grewcock (Bath), 19 Joe Worsley (London Wasps), 20 Andy Gomarsall (Gloucester), 21 Phil Christophers (Bristol Shoguns), 22 James Simpson-Daniel (Gloucester).
Kick-off: 17.30 GMT (18.30 France)