Di Matteo has been appointed the new Villa manager with Steve Clarke coming in as his assistant.
The former Chelsea and West Bromwich Albion boss succeeds Remi Garde, who parted company with the Villans in March.
Villa will play in the Championship next season after getting relegated from the Premier League at the end of the 2015-16 campaign.
Di Matteo knows the league well, having guided West Bromwich Albion to promotion from the Championship to the Premier League.
Former Villa prospect Graham, who is now at Championship side Wolves, is pleased with the decision of the Villans to appoint Di Matteo as the manager.
Lewis Kinsella, who is on the books of Villa at the moment but will leave at the end of the month when his current contract runs out, has also backed the Italian to succeed at Villa Park.
Great appointment for Aston Villa, can't wait for next season now. Just hope the fixtures list is kind to me— Jordan Graham (@JordanG_14) June 3, 2016
Great signing for villa wish them the very best hope they can come straight back up— Lewis Kinsella (@Lewis_kinsella) June 3, 2016