The Scot, runner-up the tournament in 2012, coasted to victory in one hour and 13 minutes over the unseeded Spaniard, ranked No. 35 in the world.
Murray improved to 13-1 in matches against Verdasco.
"It's always nice to win any tournament, but especially ones you haven't won before," Murray said in his on-court interview televised by Sky Sports 4 after the match. So obviously I'm very happy to do it here for the first time. It's been a good start to the year.
"It's been quite a few late finishes this week and maybe the last couple of matches I didn't start as well as I would have liked. But it's been the same for all of the players. It's been a tricky week with the drizzle and the rain and the matches starting a bit later, but once I got going today I was moving well and I finished strong."
It was a sluggish start for both players on a crisp evening at the Aviation Club. Verdasco broke Murray to open the match, but three unforced errors by the Spaniard handed the advantage right back.
It marked Murray's 121st consecutive match in which he has broken his opponent's serve.
Murray opened a 5-3 lead, then served out the first set, and the top seed continued to dominate in the second set to secure his 45th tour-level title.
Verdasco was bidding for his eighth ATP World Tour title in his 22nd final.