Telford have moved to appoint a temporary management team after Gavin Cowan departed the club via mutual consent yesterday following more than three years in charge.
Experienced boss Greene, 56, most recently managed Tamworth who he left in January 2019. He will be assisted by Meechan, 41, who had a stint as joint-boss at Stafford Rangers a couple of years ago.
Former attacker Meechan helped the Bucks win promotion to the top tier of non-league in the 2010/11 campaign. He featured 32 times in the promotion-winning season, where Andy Sinton's side saw off Guiseley in the play-off final in front of more than 5,400 supporters to return to the Conference.
A statement from the board of directors said: "Both bring a wealth of experience and knowledge of the National League North.
"Let's together get behind the first team and the football club for the upcoming games."
The temporary duo will take charge of training tomorrow evening and Saturday's trip to Spennymoor. It is likely they club be in place for Telford's trip to Greene's former club Boston next Tuesday.
The move comes as the club, who sit 20th in National League North, begin a 'detailed' recruitment process that they say could take 'some time'.
It is understood the duo take the reins at the New Bucks Head with an eye very much on the short-term, with the club inviting applicants to replace Cowan before a deadline set for Friday.