Villa announced on Friday that Vlaar would be signing for them after agreeing personal terms - subject to passing a medical - and that has been successfully completed.
The fee is understood to be around £3million and centre-back Vlaar, part of his country's Euro 2012 squad, becomes Villa's fourth signing of the summer. It is also the second player new Villa manager Paul Lambert has signed from the Rotterdam club after the arrival of midfielder Karim El Ahmadi, also for around £3million.
Vlaar held talks with Lambert earlier in the month and he said goodbye over the weekend to his Feyenoord team-mates before linking up with Villa at their Bodymoor Heath training complex on Tuesday.
Vlaar, 27, broke into senior football with AZ Alkmaar before joining Feyenoord in 2006. He had initial injury problems at Feyenoord and was sidelined for almost two years with two cruciate ligament setbacks.
But during the past three years he has been a key figure for Feyenoord. He formed an impressive partnership with Brazilian defender Andre Bahia and helped his club make sure of their place in qualifying for next season's Champions League.
Vlaar made his international debut under Marco van Basten seven years ago.
His arrival at Villa comes on the day fellow centre-back James Collins completed a return to West Ham.
Winger Brett Holman (AZ Alkmaar) and right-back Matthew Lowton (Sheffield United) are the other arrivals at Villa so far this summer.