Di Matteo, who managed Chelsea, West Brom and Schalke, replaces Remi Garde, who was sacked in March prior to the club’s relegation from the Premier League.
The 46-year-old, and former West Brom and Reading boss Clarke, 52, have been out of management since last year.
Di Matteo, who guided Chelsea to Champions League success in 2012, was always the first choice of Chinese Xia Jiantong, who bought Villa two weeks ago.
Former Leicester manager Nigel Pearson was also linked to the job but he was announced as Derby County manager earlier.
Another option David Moyes, the former Manchester United boss, chose to rule him out for the job.