Bryant completed the event at 16-under-par 272. For Bryant, it was his second win on the PGA Tour. His other win came at the 2004 Texas Open.
Fred Couples, the 1998 Memorial winner, carded a final-round 69 to finish alone in second at minus-15.
Tiger Woods, a three-time Memorial winner, matched Bryant's 68 to move into a tie for third at 12-under-par 276. He was joined there by Bo Van Pelt and Jeff Sluman, who held at least a share of the lead after each of the first three rounds at Muirfield Village Golf Club.
Bryant, one of four leaders entering the round, had an up-and-down front nine. He birdied the second to take a one-stroke lead. He tripped to a bogey at the next though to fall one behind Sluman and Couples.
The 42-year-old Bryant grabbed a piece of the lead with a birdie on five. He stumbled to a bogey at the next though. He joined Couples atop the leaderboard again with a birdie on No. 7.
Bryant again dropped one back with a bogey on the eighth. After a pair of pars, the New Mexico State graduate moved to 13 under with a birdie on No. 11. With that, he tied Richard Green in the lead. Bryant sank a birdie try on 14 to again tie Couples for the lead.
After a Couples birdie, Bryant matched him with a birdie on 15. He rolled in a birdie attempt at 16, his third straight, to move one stroke clear of the field.
Bryant's drive at 18 found a hazard left of the fairway. He took a penalty drop, then knocked his third shot to 12 feet. He sank that putt for his par to remain one shot clear of Couples, who was in the fairway behind him. Couples was unable to catch him however.
'I feel really good. I'm very blessed to win here, my second win,' said Bryant, who earned $990,000 for the win. 'It'll be able to validate what I did last year.
'But to win against a quality field like this on a great, great golf course, I said it before and I'll say it again, but as a PGA Tour player, to walk off the 18th green and have Mr. Nicklaus waiting to shake your hand and congratulate you is beyond comprehension at this point, it's really cool.'
Couples opened with a birdie on the second to tie Sluman for first place. He tripped to a bogey on No. 5, but managed to retain a piece of the lead. The former Houston Cougar slipped back to 11 under with a bogey on eight.
The 45-year-old responded with a birdie on No. 9 to get back within one of the leader. Couples joined Bryant and Green at 13 under with a birdie on the 11th. He came right back with a birdie on 12 to move one clear of the field.
Couples dropped in back-to-back birdie putts from the 14th to stay one ahead of Bryant. The 1992 Masters champion faltered to a bogey on 16 though to fall one back of Bryant.
Couples parred the 17th after hitting his second to the green from an awkward stance on the side of a fairway bunker. He two-putted for par. Couples' drive on 18 split the fairway.
He needed to birdie that hole to force a playoff though. He knocked his second long and left of the pin. He blasted his third out of thick rough, but it rolled by the hole. Couples drained his par putt to finish one back.
Woods traded a birdie for a bogey from the second. He later ran off three straight birdies from the fifth to jump to 11 under and get within two of the lead.
His run stopped with a double bogey on No. 9 though. Woods dropped in a birdie on the 11th and made it two in a row with a birdie at 12.
Woods fell three behind the leaders after a bogey on 14. He tried to get back into contention with birdies on 15 and 17, but fell short. With the tie for third, he will remain No. 2 in the world behind Vijay Singh, who missed the cut here. If Woods had finished alone in third, he would have overtaken the Fijian.
Jonathan Kaye and Nick O'Hern shared sixth place at 11-under-par 277. Lucas Glover, Green, K.J. Choi, Jim Furyk and David Toms were one stroke further back at minus-10.
Ernie Els, the 2004 champion, was never a factor this week. He eagled the par-5 15th in the final round, but bogeyed the last two holes to close an even-par round of 72. He finished at even-par 288 in a tie for 45th.