Roma, who have dropped to fifth in Serie A after leading earlier in the season, said he would stay until the end of the season for a fee of 1.4 million euros (1.05 million pounds).
The 23-year-old, who has made 17 appearances for Italy, had spent the first half of the season on loan at AS Monaco where he failed to score a goal in 15 Ligue 1 outings.
"I'm very determined and excited, Roma is a fresh start for me," he told Roma's website. "I've come here with a lot of humility to try and turn my career around."
He was also looking to get back into the Italy squad in time for Euro 2016.
"To be called up for the national team you need to be playing regularly at club level and to do that you need to work hard, be committed and show desire. My aim is to play well for Roma to achieve that."
El Shaarawy joined Milan in 2011 and found his scoring touch in the 2012/13 season, where he was Serie A topscorer with 14 goals at the halfway mark.
However, he scored only two more goals that season after the club signed Mario Balotelli in the January transfer window.
He missed almost the whole of the 2013/14 season due to a foot injury which failed to heal after surgery and suffered another foot injury which also sidelined him for much of last season.
Roma said the agreement included an option to make the deal permanent, for a fee of 13 million euros, before the beginning of the 2016-17 season.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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