Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The Irishman will sign a two-year contract for the Irn-Bru Third Division champions on September 1, when their transfer embargo expires.
Daly, who had confirmed his intention to sign for Rangers on Sunday, follows Kilmarnock goalkeeper Cammy Bell and Motherwell midfielder Nicky Law in joining the Ibrox side this week.
The 30-year-old was out of contract at Tannadice and had captained the club this season.
Daly, who has also played centre-back for United, scored 72 goals in 203 appearances after signing from Hartlepool in January 2007.