Victory was Sutton's 20th in 25 games since their last league defeat on 7 November and came one week after their vital win over second-placed Ebbsfleet.
Dan Fitchett put the hosts ahead against Chelmsford and Ross Stearn added a second before half-time.
They return to the fifth tier for the first time since relegation in 2000.
Sutton United clinched promotion to the National League as they secured the National League South title with a 2-0 home win over Chelmsford City.