In an event that saw Martin Laird claim his fourth top-10 finish in eight starts on the PGA Tour this season, Johnson toppled Jason Day in style.
The US Open champion closed with rounds of 64 and 71 on a marathon final day ay Riviera Country Club to finish clear of the field on 17-under-par.
Johnson needed to win and hope Day finished lower than a three-way tie for third to top the rankings - and the Australian could only manage a tie for 64th after finishing two over par.
“Today was a great day,” admitted Johnson, the US Open champion. “I played really good all day long and I’m very happy.
“It’s obviously a big bonus to finally get to that No 1 spot.”
The 32-year-old started the final day just a shot ahead before storming six clear with his seven-under effort in the third round.
That took him to 17-under, equalling the 54-hole record, and he was on course to threaten the 72-hole record of 20-under before stumbling to three bogeys in the final round.
“I’m very proud of myself and my whole team who have supported me,” added Johnson. “It’s going to push me to work even harder.”
Big-hitting Belgian Thomas Pieters shot a closing 63 to finish joint-second with American Scott Brown (67).
Olympic champion Justin Rose finished in a four-way tie for fourth on 11-under, a shot ahead of Laird, who had an eagle and five birdies in his closing 66.
The Scot is up six spots to 20th in the FedEx Cup standings.
Fred Couples returned to winning ways as he held jumped above Miguel Angel Jimenez in the round to claim the Chubb Classic in Florida.
The 57-year-old closed with a bogey-free five-under 67 at Twin Eagles to finish on 16-under-par, three strokes ahead of overnight leader Jimenez.
It was Couples’ 12th Champions Tour title triumph but first since 2014 after being hampered by back problems.
“It feels great,” admitted Couples as he moved to No 1 in the Charles Schwab Cup standings.
Jerry Kelly closed with a 66 to tie for third on his over-50s debut while Colin Montgomerie tied for 20th.
Paul Lawrie has jumped more than 200 spots in the world rankings after securing his first victory in more than four years.
The Aberdonian is up to 246th, a climb of 206 places, on the back of a one-shot success in the Sunshine Tour’s Dimension Data Pro-Am.
It’s the highest he’s been since sitting 254th after the Alfred Dunhill Links Championship towards the end of the 2014 season.
Martin Laird, meanwhile, is getting close to being back in the top 100 aftrer maintaining his good form with a top-10 finish in the Genesis Open in Los Angeles. He’s up seven spots to 110th.
Russell Knox, who didn’t play in the latest PGA Tour event but returns to action in this week’s Honda Classic, is down one place to 19th.
After Knox and Laird, Marc Warren is the third highest-ranked Scot in 241st, followed by Lawrie then Richie Ramsay (279th), Stephen Gallacher (309th) and David Drysdale (312th).
A brilliant eagle-birdie finish handed South Korea’s Ha Na Jang the ISPS Handa Australian Women’s Open title in Adelaide.
Edinburgh-based American Beth Allen finished in a tie for seventh at five-under, five behind the winner, after shooting a three-under 70 in windy conditions at Royal Adelaide.
Allen, who finished in a tie for fourth at last year’s Australian Open, said she was pleased to get her LPGA season off to a strong start.
“I know I can play out here, I think I’ve proved that,” she said. “I’m looking forward to see what happens next but I’m happy to have a top 10 to start.”
The 35-year-old will fly back to Scotland this week before heading to the United States for the Bank of Hope Founders Cup in Phoenix in he middle of next month.
Playing in their first LPGA tournament, Scottish rising stars Michele Thomson and Gemma Dryburgh struggled in the windy weekend conditions after strong opening rounds.
Thomson finished on in a tie for 64th on six-over, a shot ahead of Dryburgh in joint-66th.
Defending champion Craig Ross was among three Scots to make encouraging starts in the stroke-play qualifying for the South African Amateur Championship at Humewood.
The Kirkhill player carded a bogey-free three-under 69 to sit joint-26th, behind both Liam Johnston and Calum Fyfe as they signed for 67 and 68 respectively.
Banchory’s James Byrne chalked up a top-10 finish in the Asian Development Tour’s PGM Panasonic Malaysia Championship.
The former Walker Cup player carded rounds of 71-66-72-66 for a 13-under total in an event won by American Brett Munson.