Valverde (Movistar) outsprinted Miguel Angel Lopez (Astana) atop the decisive 10.8km Jebel Hafeet climb to take the red jersey from overnight leader Rohan Dennis (BMC Racing), who slipped to ninth.
Wilco Kelderman (Sunweb) finished second overall, 17 second adrift, with Lopez third.
Stage four winner Dennis had tipped 37-year-old rival Valverde would be the man to watch on the last day, and the Australian was right.
“When he looked back at one stage, I wasn’t feeling too good and he wasn’t even breathing,” Dennis said. “Hats off to him, he’s a classy rider and he deserved to win today.”
Valverde arrived in Abu Dhabi early ahead of the race to acclimatise, recover from jet-lag and recon the climb three times over two days.
“I knew the climb, I studied the places where I might try to attack,” the Spaniard said.
“Now I can tell it was a really good idea to come before because thanks to that I was able to win the stage. I knew exactly when I had to attack.
“It’s a really important win for me, the team and our motivation.”
A nine-man break surprisingly including marquee sprinter Andre Greipel (Lotto Soudal) animated the first part of the 199km stage before the escape began to disintegrate on the early slopes of the ascent.
Greipel called it with 7.4km remaining, leaving Lawson Craddock (EF Education First-Drapac) at the front of the race until the main group closed in with about 6.3km left.
Rafal Majka (BORA-hansgrohe) and Julian Alaphilippe (Quick-Step Floors) followed an attack from Valverde, as Craddock drifted back and Dennis began to lose contact, pacing behind teammate Brent Bookwalter.
Tom Dumoulin was dropped with 5km remaining and prior to a mechanical that, for the second consecutive day, took him completely out of the frame, the Dutchman throwing his bike on the roadside in frustration.
Valverde accelerated again with about 3km to go, bridging to Lopez, who he outsmarted and came around on the home straight.
“There is no secret, it’s my physical condition,” the veteran said of his shape.
“I love what I do, it’s my work but it’s my passion, and if I continue winning I will continue riding.
“I started in Mallorca with really good feelings, could confirm in the Tour of Valencia I was in really good shape and up until now.
“I am really happy with what I’m doing, my team, all the guys I have around me. I know I’m a rider that gets big wins during the season and I’m always there.”