Lawson began his career with Celtic, where he played four times for the first-team, and also enjoyed loan spells at St Johnstone and St Mirren before joining Ross County in the summer of 2007.
The 28-year-old said: "It's great to have my future sorted out. There is a lot of uncertainty around Scottish football so it's really pleasing to have things sorted early doors.
"I enjoyed my time at Ross County. I have been pleased with my performances and thankfully the manager [Stuart McCall] spotted that and came in to sign me.
"He is probably the main reason why I joined. I met him and he was keen to bring me here which was great and obviously the boys have enjoyed a fantastic season and I am keen to try and continue that next year."
Motherwell have also confirmed that Darren Randolph, Steven Saunders, Nicky Law, Omar Daley, Steven Hetherington, Josh Watt and Nicky Devlin are all leaving Fir Park.