The US Open champion took the lead in the second round and never relinquished it, ending the weekend 17 under par and winning by five shots at Riviera Country Club.
Johnson needed to win and hope Jason Day finished lower than a three-way tie for third to top the rankings – and the outgoing number one could only manage a tie for 64th after finishing two over par.
The leaders had to complete two rounds on Sunday, following storms on Friday.
Johnson took to the course on day four with a one-shot lead but was six strokes clear after the third round.
The 32-year-old started with a birdie on the first and picked up further shots on the fifth, eighth and 12th before birdieing the last three holes for a seven-under 64.
That took him to 17 under for the tournament – equalling the 54-hole record.