The 31-year-old will move to Kingston Park from Falcons' Aviva Premiership rivals Gloucester.
He becomes Newcastle's third key signing in the last few days, following locks Carlo Del Fava and Scott MacLeod.
Newcastle finished bottom of the Premiership this season, but their fate rests on the outcome of the two-legged RFU Championship final between Cornish Pirates and London Welsh later this month.
The Rugby Football Union and Premiership Rugby are likely to announce early next week whether or not London Welsh meet Premiership entry criteria. The Pirates did not put themselves forward for audit.
Newcastle, who will be led by newly-appointed rugby director Dean Richards next season, are set to announce further signings during the coming days.
Lawson has won 30 Scotland caps, making his debut against Australia in 2006 and has been part of two World Cup campaigns. He has also captained his country.
"I am really looking forward to joining up with the Falcons this summer," Lawson told Newcastle's official website.
"Newcastle's form towards the end of the season was strong, and there is a lot we can build upon for next year to move the club forward.
"Having met with (club owner) Semore Kurdi it is clear that the Falcons have significant resource and intent to build a successful club in the north-east, and the appointment of Dean Richards can only enhance that."