Watt joined Arsenal as a scholar in summer 2007, signing professional terms with the Gunners a year later in summer 2008.
His fine performances were rewarded last November, when he signed a new long-term contract with the club.
The England U-19 international winger enjoyed a successful spell on loan at Elland Road last season, playing six games to help United clinch promotion from League One.
Watt is the club's eighth summer signing and is likely to temporarily fill the gap left by Robert Snodgrass, who is out for around a month due to a knee injury.
Simon Grayson was pleased with the signing, and said: "We're delighted we've been managed to bring Sanchez back. He did well last year and he's another good addition to our squad. He's a young and up and coming player who has plenty to offer and his arrival will only increase the competition for places."
Watt, who spent February of last season on loan at Southend United, will immediately join up with Simon Grayson's squad ahead of the new season.
Meanwhile, Tom Lees has left Leeds for Bury on a loan deal until January.
Source: PA
Source: PA