The 23-year-old forward, who earned a move from Albion Rovers to English big guns Sunderland in January 2018, will arrive at Fir Park on a three-year deal in June, when the transfer window officially opens.
Shields, who scored eight times in 22 Scottish Championship games for the Doonhamers last season, is the first summer capture for ’Well boss Graham Alexander
Alexander told the club website: “We’re very happy to bring Connor in to start our rebuilding for next season.
“He’s had a great year scoring goals in the Championship and we believe he has the potential to do the same in the top flight.
“He’s quick, works incredibly hard and is hungry to prove himself at a higher level.
“He now has that opportunity and we’re really looking forward to working with him.”
Shields’ arrival will likely be the first of many new additions at Fir Park, with the club having just released 17 first team players including established stars like Allan Campbell, Declan Gallagher and Chris Long.
"We have got a bit of recruitment to do,” Alexander said. “I would guess between seven and 10 additions to the squad.
"I’m not big on carrying a big squad. I feel you have too many demontivated players who are not close to the first team.”
Several loanees from last season have also departed, although Alexander is reportedly in talks with Blackburn Rovers about the possibility of defender Tyler Magloire returning to ’Well on loan for next season.
He would also be keen on bringing keeper Liam Kelly – outstanding last term after joining on loan from QPR in January – back for another spell between the sticks in Lanarkshire.
Last week’s group stage draw for the newly named Premier Sports Cup – formerly the Betfred Cup – put ’Well in Group F with Queen of the South, Airdrieonians, Annan Athletic and Queen’s Park.
The first match falls on the weekend of July 10/11.