Coyle, sacked as Bolton boss last October, has been selected by Latics chairman Dave Whelan having beaten off competition from close to 50 applicants, with former England coach Steve McClaren also understood to have been among a final shortlist of three or four candidates.
A statement on Wigan's website read: "Wigan Athletic are delighted to confirm the appointment of new manager Owen Coyle.
"Following discussions with the club on Friday afternoon, the 46-year-old has now agreed terms to become the 37th manager of the club and begins work immediately."
The Scot's appointment comes 10 days after Martinez's departure was confirmed as he took up the managerial vacancy at Everton following four years in charge at Wigan.
Martinez led the club to memorable FA Cup glory last season but opted to leave after they also suffered relegation from the Barclays Premier League.
Coyle's main priority next term will be to secure an immediate return to the top flight although he will, however, also have Europa League football to contend with for the first time in the club's history.
Earlier he told Sky Sports News: "Everybody recognises Wigan as a fantastic club with a chairman who wants to get back in the Premier League.
"It was a blow to lose that status and we will look to get it back as quickly as possible. It's a great opportunity and one I am looking forward to."