The 19-year-old left-back, a product of the club's youth academy, is now reunited former Saddlers boss Dean Smith after agreeing a deal with the Bees.
Walsall had been desperate to hold on to Henry, who has been scouted by a host of clubs in the Premier League and Championship, even turning down a seven-figure bid from an unnamed club 12 months ago.
But with Brentford prepared to meet their valuation and Henry keen to play at a higher level, the Saddlers have agreed to let him move on.
"Rico has done tremendously well for us and is capable of playing at a higher level," said manager Jon Whitney. "He feels he is ready to test himself in the Championship and the offer made was one which we feel meets his valuation both now and in the future with the numerous add-ons included.
"He leaves with our best wishes and we will now look to the next group of players to continue to push the club forward.
"We've built up a proud history of developing young players and will continue with this philosophy."
The terms of the deal will see the Saddlers receive an initial £1.5million fee, which could rise to more than £5million dependent on numerous add-on clauses.
Henry, who joined the club as an 11-year-old, signed his first professional contract in 2014 and made his debut during the 2014/15 campaign.
Last season he was integral part of the Saddlers team which missed out on automatic promotion by a single point and was named the club's young player of the season, in addition to featuring in the League One team of the year.. He leaves the Banks's having made 57 appearances in all competitions.