The 25-year-old, who scored in the Promotion Final earlier this month, moved to the League Two club on a two-year deal.
Both Sbarra and Doncaster will kick-off the 2024-25 season looking to put play-off failure behind them and will look to go one better next time.
Grant McCann moved fast to seal the deal and the midfielder, who scored 36 goals in 149 appearances for Solihull last season. Sbarra said: “From the first conversation with the gaffer, everything he had to say appealed to me loads.
“The way he plays suits me and the way he sees me fitting in. How welcoming him and his staff have been has been great as well so I’m really pleased.”
Andy Whing is hoping his exit won’t damage the club’s chances of getting over the agony of a “season of fine margins”.
The club lost the FA Trophy on penalty kicks last Saturday, six days after Bromley defeated them in the National League Promotion Final on spot-kicks.
“Everybody thought we'd be bottom half,” he said. “But the lads have been brilliant all season. The whole squad has shown great character over our 56 games.
"Nobody was expecting us to get to two finals. But we've just got to learn from this experience. It will drive us on.
"We have a good blueprint, the recruitment has been fantastic and we're now looking forward even more to the future."