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, who was part of his country's UEFA EURO 2012 squad, becomes Villa's fourth signing of the close season.
He is also the second player new Villa manager Paul Lambert has signed from the Rotterdam club following 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.
The 27-year-old broke into senior football with AZ Alkmaar before joining Feyenoord in 2006. He had initial injury problems 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 UEFA Champions League. Vlaar made his international debut under Marco van Basten seven years ago.