The 23-year-old scored 19 goals in 30 matches in all competitions for the Mariners this season, prompting a reported flood of interest by a host of clubs.
Latics boss Warren Joyce told the official site: "Omar is a finisher, and he has scored goals at every level he has played at.
"He needs to take it to the next level now but we are convinced he has the attributes to be a success here."
Bogle, who was said to be on the radar of Nottingham Forest and Rotherham United among other second-tier clubs, has scored 35 goals in 78 appearances in all competitions for Grimsby.
He began his career at West Bromwich Albion, Birmingham City and Celtic before turning out for a number of non-league sides.