The vastly experienced Wilcox, 59, replaces Neal Bishop, who stepped down earlier this month citing personal reasons.
After a full and thorough recruitment process over the last 10 days, the Holy Blues have identified former Farsley Celtic manager Wilcox as the man to take them forward.
He helped his former club avoid relegation on the last day of the 2022/23 National League North season but quit less than a month later, after less than 18 months in charge.
Last season, Wilcox also helped Farsley reach the FA Trophy quarter-finals - the furthest the club have ever gone in the competition.
After a long and distinguished playing career which came to an end in 2003, he enjoyed a brief spell as caretaker manager of Scunthorpe United.
He also took the helm at York and was previously an assistant to Brian Laws at both Sheffield United and Burnley.
Following his appointment, Wilcox said: "We want supporters leaving with smiles on their faces. It's ultimately a results business and we'll be doing everything we can to get results.
"We have only had seven games so far, there are 35 games left to play, and anything can happen in football.
"I've seen a lot of the games, but I'm really looking forward to getting down to business with the group. Everyone starts with a clean slate and the opportunity to impress."
Gainsborough have endured a difficult start to the new Northern Premier League season, with just one win from seven matches leaving them in the relegation zone.
Wilcox's first game in charge will be at home to Atherton Collieries on Saturday.
Trinity CEO Matt Boles said: "We are absolutely delighted to secure a manager of the calibre of Russ.
"His experience and reputation within the game speaks for itself. We believe this is the right appointment for the club and are delighted that Russ has accepted our offer to become first team manager at Gainsborough Trinity.
"Having interviewed Russ and having a number of subsequent discussions, it is clear that his passion and vision to take our club forward is something we should all be excited about.
"I look forward to working with Russ and helping to deliver our objectives for the club and the fans."
Photo credit: Gainsborough Trinity