He became just the second Spaniard, after Seve Ballesteros to top the rankings.
He has now replaced Rory McIlroy as world number one after the Derryman finished back on four over, after a 78 yesterday.
Rahm had a four-stroke lead heading into the final round, and it appeared through the front nine that he was cruising to victory.
He suffered a bogey on 10th though which changed the direction of things. He then shot a double bogey on the 11th before losing another stroke on the 14th.
The biggest moment of the day came on the 16th hole, when an up-and-down birdie was overturned when PGA Tour officials reviewed his chip and deemed the ball moved when Rahm placed his wedge behind it.
This resulted in a two stroke penalty but it did not seem to affect him as he got back-to-back pars on the last two holes.
2016: Jack Nicklaus Award winner
2020: @MemorialGolf winner pic.twitter.com/M7HeiyIAc8— PGA TOUR (@PGATOUR) July 20, 2020
Speaking to Sky Sports News after his win, Rahm said he's dedicating the win to relatives lost during the coronavirus pandemic.
"Anytime I can join Spanish history with Seve it is unbelievable. Unfortunately I lost two family members in this quarantine.
"I haven't be able to go to the funeral but my grandmothers ashes were put next to my families in Madrid yesterday.
"I am happy I could do this for my mom and grandmother and the rest of my family."
