Middlesex star Shah pipped Young Cricketer of the Year Ravi Bopara to the last batting spot after a prolific campaign.
Uncapped Nottinghamshire spinner Swann has been chosen to back up Monty Panesar and Sussex wicketkeeper Matt Prior has also been recalled.
With former captain Michael Vaughan not considered due to a lack of form, Shah will get the chance to fight for a third Test cap.
His debut came in India two years ago when he stepped in for the ill Alastair Cook and struck an imperious 88 in the series-levelling victory in Mumbai.
"Our decision to pick Owais Shah was based on the fact that he is an excellent player of spin who played a superb innings in India on his Test debut two years ago," said national selector Geoff Miller.
"It's a further opportunity for him to build on his success with the one-day side this year and his inclusion in the squad will create real competition for places within the batting unit."
It is anticipated that Prior will now assume the role of number one gloveman in all forms of the game, and the four-man selection panel have sought to emphasise their faith in Tim Ambrose as his most natural competitor by adding him as limited-overs cover for the seven-match series which precedes the Test tour.
That is a move which will disappoint supporters of James Foster, who has built a strong case for a recall. According to the England camp, he was not picked for either the full tour or in the performance squad due to a shoulder injury.
"Matt Prior has enjoyed an impressive domestic season with Sussex and having re-established himself in the England one-day side, he will now compete with Tim Ambrose for the position of Test wicketkeeper," said Miller.
"Matt remains our first-choice keeper in the one-day game, but Tim will join the squad in India as reserve wicketkeeper for the duration of the one-day series."
With a second-string side also on the subcontinent during the tour and linking up with the full party for the second Test in Mumbai, England resisted the temptation to add a third spinner, relying on off-spinner Swann.
Yorkshire all-rounder Adil Rashid, whose leg spin reaped 62 wickets in Division One of the County Championship, will be among that group of developing players on standby for the Tests should injury or illness strike.
"The inclusion of Swann as off spinner provides us with a right-arm/left-arm slow bowling combination which we believe can be effective in India," added Miller.
"Graeme has bowled well in tandem with Monty Panesar when they were at Northamptonshire together and he will be keen to renew the partnership this winter."
England travel to India ahead of the first Test in Ahmedabad on December 11. The second Test begins in Mumbai on December 19.
England's 15-man squad for the two-Test tour of India:
Kevin Pietersen (capt, Hampshire), Tim Ambrose (wkt, Warwickshire), James Anderson (Lancashire), Ian Bell (Warwickshire), Stuart Broad (Nottinghamshire), Paul Collingwood (Durham), Alastair Cook (Essex), Andrew Flintoff (Lancashire), Steve Harmison (Durham), Monty Panesar (Northamptonshire), Matt Prior (wkt, Sussex), Owais Shah (Middlesex), Ryan Sidebottom (Nottinghamshire), Andrew Strauss (Middlesex), Graeme Swann (Nottinghamshire)