Espinoza got his visa on Thursday and has now flown into England to complete the finishing touches on a two-and-a-half-year deal.
"I am just so happy to finally be here," the Honduras midfielder said. "It's taken a while to get all the paperwork done but now I can concentrate on fighting for my place and helping the team."
Espinoza starred alongside another Wigan man, defender Maynor Figueroa, during Honduras' Olympic campaign.
Martinez has kept a keen eye on the 26-year-old ever since and has now snapped up the midfielder, a US citizen, from Kansas City Wizards.
And while he accepts it is hardly ideal, Martinez realises he has little option other than to hand Espinoza his debut at the DW Stadium on Saturday, where loan signing Angelo Henriquez will also be involved for the first time.
"Usually players would have more time preparing for their debut and getting used to their new team-mates, but Roger is so desperate to play as soon as he can that we hope to see him on the pitch on Saturday," Martinez said.