Chopra deputised as skipper for the injured Jim Troughton in 2014 and led Birmingham Bears to NatWest T20 Blast glory on home soil at Edgbaston and the Royal London One-Day Cup final.
Having been appointed on a permanent basis following the retirement of Troughton, Chopra guided the Bears back to Finals Day in his first full season in charge last term.
But the opening batsman’s form dipped as a result and, having hit only 658 runs at an average of 27.41 in the County Championship last season, has decided to relinquish the role with immediate effect.
Chopra said: “I have thoroughly enjoyed my time as captain of the Bears and regard our NatWest T20 Blast success in 2014 as one of the best moments of my career.
“Whilst it has been a difficult decision to make, I feel that focusing on my batting is in the best interests of the team and I’m looking forward to fully supporting Ian, scoring as many runs as possible and hopefully contributing to more success in 2016 and beyond.
“I would like to thank the players, coaches and members for their support throughout my tenure.”
Five-time Ashes winner Bell, who has played 118 Tests, 161 one-day internationals and eight Twenty20s for England, brings a wealth of experience to the role
Warwickshire director of cricket Dougie Brown added: “Varun has been one of the most prolific batsmen in the county game since he joined the club and he has made a huge contribution as an opener and captain, scoring 14 first-class centuries and helping us transform in to one of the top T20 sides in the country.
“As a team we fully understand and respect his decision to focus on his batting at the top of the order to help the team get off to the best possible start.
“In Ian Bell we have one of the most celebrated cricketers in the club’s history, who has worn the Bear and Ragged Staff since the age of 10 and has played at the very highest level of the game since 2004.
“He is an excellent role model for the younger members of the squad and will build on the great work that Varun has done in leading Warwickshire and Birmingham Bears with huge pride and proficiency.”
Bell has previous experience of leading Warwickshire after captaining the side to the Clydesdale Bank 40 title at Lord’s in 2010, hitting a match-winning century.
The right-handed batsman, who has been at the club since the under-11 age group and made his senior debut in 1999, said: “The club and Edgbaston have been a huge part of my life since an early age and, in the past, I have made no secret of my desire to captain the Bears.
“I am very proud to now be given the opportunity to lead this exciting squad and to challenge for titles in all forms of the game.
“We have a strong programme of pre-season fixtures ahead and we will all be working very hard to ensure that we’re in the best possible shape for the first game of the County Championship away to Hampshire on April 10.”