A Football Association panel gave the 26-year-old the green light to join Roberto Martinez's men when his contract with MLS side Sporting Kansas City expires at the end of December.
He will become the second Honduran in the Latics squad, joining Maynor Figueroa.
Martinez said: "We prepared an excellent case for Roger and it is great news for us that he can now join up in January.
"He is a player we have been following closely since June 16 2010, when he made his debut in the World Cup versus Chile.
"In that game, he showed tremendous potential and slowly he has been developing into an exciting footballer over the last three seasons in the MLS and has enjoyed terrific experiences at international level, specifically his role with Honduras in the Olympic Games.
"The games versus Spain and Brazil in that tournament showed the winning and strong mentality that he possesses which will be an important asset to our squad."
Espinoza said: "This has been a dream for me to play in England and I am so grateful for the club who have worked so hard to make this happen.
"I just can't wait now to join up with Maynor and all the guys and get to work."
The midfielder, who should be eligible for the FA Cup tie against Bournemouth, subject to receiving international clearance, was born in Honduras but moved to Kansas at the age of 12.
He became a United States citizen in 2008, but opted to play for the country of his birth and now has 25 caps, scoring three times.