Randy Jackson Divorce Approaches Finish Line More Than 4 Years Later

Randy Jackson is one big step closer to being a single man ... more than 4 years after his wife filed for divorce.

According to new docs obtained by TMZ ... the judge signed off on Randy and his estranged wife Erika's dissolution of marriage last month. The 2 will be officially divorced on February 7.

It's unclear who got what in the divorce ... the settlement's being kept under wraps.

We broke the story ... Erika filed for divorce in September 2014 after 18 years of marriage. The couple had no prenup, so it's a good bet she made out well considering the millions Randy made in his "American Idol" heyday.

Randy and Erika have 2 adult children together, so custody is not an issue.