The Blues had seen four bids for Moses rejected by Wigan chairman Dave Whelan during the course of a fractious transfer saga that had lasted since the end of last season.
Whelan had infuriated Chelsea by speaking publicly about the negotiations in a bid to drive up the price.
But Chelsea boss Roberto Di Matteo got his man at the fifth attempt after Wigan confirmed on Thursday that they had accepted an improved offer, believed to be around £9 million, for the 21-year-old.
“Chelsea Football Club is delighted to announce the signing of Victor Moses from Wigan Athletic,” a statement on the club’s website confirmed.
Chelsea didn’t announce the length of the contract for Moses, who joined Wigan from Crystal Palace in 2010 and rose to prominence after a series of impressive displays for the Latics last season.
Moses, who scored eight times in 74 league appearances for Wigan, caught the eye again in the Latics’ 2-0 defeat against Chelsea in the Premier League last weekend.
While he clearly has vast potential, Moses will have to raise his game to an even higher level at Stamford Bridge, where he will compete with the likes of Eden Hazard, Juan Mata, Daniel Sturridge and Marko Marin for a place in Di Matteo’s starting line-up.
At international level, Moses played for England from schoolboy up to the Under-21 team, but has opted to represent Nigeria at senior level and made his debut in February against Rwanda.
Moses was Di Matteo’s second signing in just a few hours, following his capture of Marseille’s Spanish right-back Cesar Azpilicueta for £7 million.