The 24-year-old Englishman, who was with Manchester United, Liverpool and Burnley as a youth, has signed a one-year contract at Fir Park.
Sutton, who scored 13 goals last season, has joined St Johnstone.
"I've asked for the number nine jersey as I like the pressure of expectations," said Fletcher.
"I know the previous player wearing that number scored a lot, so my target is to not only match that but get more.
"I'm a player who will work hard and I know where the goal is."
Fletcher, who had spent spells on loan to Grimsby Town, Stockport County, Accrington Stanley, Crewe Alexandra and Yeovil Town, scored seven times in 32 appearances last season as York finished 18th in England's League Two.
He finally left Burnley permanently to join York in 2013 but was out of contract and was released this summer.
His arrival at Fir Park follows quickly after the addition of David Clarkson, the striker released by Dundee.
Manager Ian Baraclough told his club website: "I've seen a fair bit of Wes and know exactly what he is capable of.
"The club has also had him watched on several occasions and feel he is ready to add something different to our squad.
"His game will suit the way we want to play and, along with David Clarkson, will add more competition.
"This is just the beginning of the recruitment process though.
"We've still got several more faces to come all across the park and we'll continue to work hard to do that as quickly as possible."
Wes Fletcher has joined Motherwell after leaving York City and targeted more goals than his predecessor in the number nine jersey, John Sutton.