The Chargers had been set to pick No. 28 but traded up to get Mathews.
Mathews is expected to replace Tomlinson, who was released in February after nine brilliant seasons in which he became one of the greatest running backs in NFL history.
The Chargers saw a player they really wanted and made sure nobody else would scoop him up. San Diego made the trade with Miami, trading up from the 28th spot in the first round to the 12th spot.
The former Bulldog Mathews is widely regarded as the second best runner in the draft, behind C.J. Spiller, who went eighth to Buffalo.
With LT gone and Darren Sproles still not signed, the Bolts had a glaring need at running back. Mathews is a bruiser, 6 feet tall and 218 pounds. His stock really went up after a tremendous workout at the NFL Combine in February.
Interestingly, Mathews wore number 21 at Fresno State in honor of his favorite player, LaDanian Tomlinson.
The entire trade details: San Diego and Miami swap first-round picks, the Chargers send their second-round pick to the Dolphins, the teams swap fourth-round selections, the Chargers get a sixth-rounder and Miami gets linebacker Tim Dobbins, who the Chargers just signed to a one-year contract earlier this week.