Almagro was given a free pass in to the final of the ATP 250 event in Houston when American Sam Querrey withdrew due to a back problem, while Verdasco defeated Santiago Giraldo of Colombia 6-4 7-5.
A pinched nerve in Querrey's lower back forced the 26-year-old American to pull out of his semi-final against third seed Almagro after he woke up Saturday morning barely able to move.
In the other semi-final, fourth seed Verdasco survived a topsy-turvy second set, coming from 5-3 down against Giraldo to wrap up victory in one hour and 34 minutes.
Verdasco had won the last three games in the opening set to claim it 6-4 but found it much more difficult against his Colombian opponent in the second set.
Giraldo dropped serve in the opening game but broke straight back before holding to take a 2-1 lead.
Verdasco edged ahead in the fifth game when he broke the world number 84 but Giraldo responded immediately yet again and went on to win three consecutive games to have a chance to serve for the set at 5-3.
The 26-year-old Colombian led 15-0 and 30-15 but could not hold serve, as Verdasco recovered to win four straight games and clinch a spot in the final.
Both Almagro and Verdasco will play their first ATP finals of the year on Sunday with the former having finished runner-up at the event last year after a loss to John Isner in the decider.
Almagro has not won a title since 2012, while Verdasco's trophy drought has almost reached four years.