Police had been called to reports of a crash involving a Kia Sportage close to Bolton West Services at around 12.45pm on Sunday (June 28).
The car had been travelling southbound when it left the carriageway and overturned.
The driver of the car has now been named as mum-of-four Toni Shepherd, 38, from Lostock Hall.
Police said Ms Shepherd suffered fatal injuries and was pronounced dead at the scene.
In a tribute, Toni's family said: "Toni was a much loved daughter, sister, partner and friend but her most important role in life was as a wonderful mum to her four children.
"Toni was a ray of light in the lives of all who knew her and she was so kind hearted and trusting seeing the good in everyone.
"What she lacked in confidence she made up for in sheer determination and she worked hard at whatever she put her mind to.
"She's been taken from us far too soon and at a time when she was at her happiest.
"She will be greatly missed and we would like to ask for privacy at this incredibly difficult time."
The M61 was closed for more than four hours while accident investigators attended.
Police are continuing to appeal for information and urging any witnesses or motorists with dashboard mounted camera footage to come forward.
Sgt Chris Evans, of Lancashire Police’s Tactical Operations, said: "These are tragic circumstances and my thoughts are with Toni’s family and friends at this very sad and difficult time.
"We would encourage any witnesses, or any drivers with dashcam footage which might show the incident, to come forward if you can assist our investigation."
Anyone with information can call Lancashire Police on 101 or email [email protected] quoting log 0643 of June 28.