Daly will seal his switch when Rangers' transfer embargo ends on September 1, joining goalkeeper Cammy Bell and midfielder Nicky Law, who also committed their future to the club.
The versatile 30-year-old can also play in central defence, but he made his name as a frontman, scoring 70 goals during his six-and-a-half year stay at Tannadice.
He has netted three goals against the Light Blues, including one in United's 3-0 Scottish Cup win in February.
The Irishman started his career at Stockport and had spells in the lower leagues in England before seeking a new challenge north of the border with United in 2007.
He finished last season with 15 goals in 44 appearances.