A product of the Bolton Wanderers Academy since joining the academy at nine, Vela signed a professional contract with the club in March 2011. At age seventeen, he was linked to Liverpool and Bolton rejected £1 million offer from Liverpool. Throughout the 2011–12 season, Vela was a mainstay of the reserve team, although he spent three months on the sidelines after fracturing his foot in a reserve match with Blackburn Rovers in November 2011. After returning to fitness, he was rewarded with a new three-and-a-half-year contract in February 2012. Vela was then given number twenty-five shirt at the club. He made his debut for the club in the 1–1 home draw against Swansea City on 21 April 2012, coming on for Mark Davies in the 90th minute. His first start for Bolton came on 28 August in the League Cup second round against Crawley Town but this full debut didn't last long, as he was taken off after seven minutes and replaced by Darren Pratley because of an injury caused by a foul from Nicky Adams. This injury would sideline Vela for four months. On his return, Vela started in Bolton's 2–0 victory at Sunderland in an FA Cup third round replay on 15 January 2013, and he made his first league start for the club at Watford on 2 February. After those matches, Vela expressed his delight on returning to action from injury. On 21 March 2014, Vela joined League One club Notts County on an initial 28-day loan. He made his Notts County debut the next day, starting in central midfield, in a 4–1 win over Carlisle United. After making five appearances for Notts County, Vela extended his loan spell with the club until the end of the season. While at Notts County, Vela stated that time at the club could give him a chance of having first team football at Bolton. Making two further appearances, Vela's loan spell with Notts County came to an end and he returned to his parent club. Upon leaving, manager Shaun Derry paid tribute to him, saying that he had "been at the centre of all our good results and he's done very well." In the 2014–15 season, Vela was initially to be sent out on loan by Dougie Freedman, but this didn't happen, as Freedman was sacked by the club. Under new manager Neil Lennon, Vela was playing at right back ahead of the more experienced Kevin McNaughton and fellow youth graduate Oscar Threlkeld. For his good displays, Vela was among the players to be offered new contracts by Lennon, as his contract was due to expire at the end of the 2014–15 season. He made twenty-nine appearances for the club this season, but impressive displays at right-back and in his return to a midfield position, led The Bolton News to call for Vela to be voted the club's player of the year, while Lennon said he should be proud of his displays during the season. At the award ceremony, Vela finished second with 19 percent for Bolton Wanderers' Player of the Season, just behind Tim Ream. Vela scored his first goal for Bolton in a 2–2 draw with Charlton Athletic on 15 December 2015. At the end of the 2018–19 season, Vela confirmed that he would be leaving the club after seventeen years. He left because his relationship with manager Phil Parkinson became irreparable as Vela refused to be on the bench and was annoyed that loan players were playing instead of him.
On 20 January 2020, Vela came back to England, signing for League One side Shrewsbury Town on a two-and-a-half-year deal. He was assigned the number 20 shirt.
