The decision comes the day after the team lost 2-0 at home to Kilmarnock, leaving the Steelmen in 10th, two points off the foot of the Premiership.
Motherwell are without a win in nine games in all competitions.
The club accepted his resignation with “regret", Robinson believing he had taken the team as far as he could.
A Motherwell statement read: “After Wednesday night’s match with Kilmarnock, Stephen approached the board, giving an honest assessment of the current situation. He then stated his desire to leave.
“It is with regret that the board accepted his resignation, having carefully considered his reasons for wanting to leave his post.
“Despite the current restrictions, the board will now run a thorough process to identify the right person to take the manager’s post.
“This will move at pace, mindful of the busy fixture list and the January transfer window’s impending opening.”
Keith Lasley, who was Robinson’s assistant, will take charge of the North Lanarkshire derby with Hamilton on Saturday.
Robinson, meanwhile, will take time away from football before deciding on his next move.
He is content he has left the club in a better position than what it was when he was appointed permanent boss in March 2017.
Robinson led the club into Europe and to two cup finals.
‘Time for someone new’
“I would like to thank everyone at Motherwell FC for their support throughout my time here, both as manager and assistant,” he said.
“We have qualified for Europe, reached two cup finals and achieved a third-place finish, on top of developing some wonderful players in my time here.
“We cleared the club’s external debt through player sales, cup runs and league positions. The club has numerous assets going forward, and I’m sure that there will have a strong finish to the season with the brilliant coaching staff currently there.
“My goal was always to leave the club in a healthier position. I believe the staff and I have done this.
“I now feel it is the time for someone new to take the club forward as I feel I have taken it as far as I can.
“I would like to put on record my thanks to Jim McMahon, Alan Burrows and the rest of the board, as well as the fans for their loyalty and support to my family and I throughout.
“I will take a short break before looking at new challenges ahead. But my family and I will forever be Motherwell fans. I wish the staff, supporters and club as a whole every success in the future.”
Motherwell chairman Jim McMahon said: “I thank Stephen for everything he has done for this club. Year after year, he delivered upon or exceeded the targets set for him.
“On the field, that entailed reaching cup finals, achieving a third-place finish and reaching European competition. Those moments will live long in the memory of supporters and will go down in our history.
“Off it, his success in player development and sales has ensured this club is in a strong financial position. His ability to rear new talent was commendable and delivered great benefit to us.
“He is a man who has conducted himself exceptionally well and has been a figurehead for our club for the last three-and-a-half years.”