The Birmingham-based side's seventh win from 14 matches this season gave them an unassailable lead at the top of the First Division table.
Ethan Bamber, Warwickshire's leading wicket-taker this season, sealed victory to finish with 5-52 and match figures of figures 9-94.
Former England all-rounder Chris Woakes provided good support with 3-38 in front of his home crowd.
A win on the third day of four secured Warwickshire's first County Championship title since 2021.
Oliver Hannon-Dalby paid tribute to the influence of veteran 37-year-old Woakes who, having retired from England duty last year, scored 228 runs and took 27 wickets in Warwickshire's cause this season.
"He could easily be sat in Saint-Tropez right now with his feet up," joked Hannon-Dalby.
"But he's here trying to win a championship for us, which says a lot about him, says a lot about what he thinks about the club, and what we're trying to do right now."
Somerset, yet to be crowned county champions, will finish runners-up for the seventh time this century after Tom Lammonby and Tom Abell both scored double hundreds against Surrey at Taunton on Saturday.