The 20-year-old academy product has made four senior appearances for the Red Devils, three of them off the bench in the Premier League and another in the Carabao Cup, but joins Lincoln in search of regular first-team football at a higher level than he has previously experienced.
Wheatley spent the first half of last season on loan at Northampton Town, scoring three goals in 22 League One appearances, before switching to Bradford City for the remainder of the campaign. He had also previously spent time on loan at Walsall in League Two, meaning his move to Lincoln will mark his fourth loan spell in the EFL and his first taste of Championship football.
"I played against Lincoln last season and didn't really enjoy it, so I'm glad to be part of the team now," Wheatley told the club website.
"I've had some loans over the past 18 months. I started in League Two, then last season League One so am looking forward to stepping up to the Championship."
Lincoln sporting director Jez George said the deal had been in the works for some time.
"This has been a signing that, for reasons out of our hands, has been delayed by a few weeks, so we are delighted to finally get it done," George explained. "Ethan can play anywhere across the top line and has a skill set that will add elite athleticism and pace, as well as technical ability, to our attacking options. He has the attributes, versatility, maturity and work ethic to make a real impact for us at the top end of our team."
The newly promoted Imps have lost both of their opening two Championship matches, scoring twice in the process, but did beat Derby County in the first round of the Carabao Cup.
Wheatley's arrival gives head coach Chris Cohen added competition up front, joining a forward line that already includes Freddie Draper and Rob Street, as well as fellow new arrivals Mason Melia and Tanto Olaofe.
Manchester United had fielded interest from several EFL clubs over the summer, along with reported approaches from Everton and Bundesliga side Schalke 04, but ultimately opted to sanction only a loan, keeping Wheatley's pathway back to Old Trafford intact.
His contract at Manchester United runs until 2028, and the club continue to view him as a prospect worth persevering with despite modest goal returns during previous loan spells in the third tier.