The 24-year old striker joined Rovers from United in the summer of 2011 but is back at Tannadice Park on a six-month loan deal which could be extended.
"I am very excited by this signing. We are not only getting an experienced international player but we are also getting someone who has a special affinity with the United fans," said Arabs boss Jackie McNamara.
"I am striving to improve Dundee United in both the short and long term and adding a player of David's quality will help achieve that.
"He has all the attributes needed by a striker and it will be a major boost to the club to have him here.
"This signing will also excite our supporters. A lot of hard work was done behind the scenes to ensure this deal went through and I have to praise the board who gave the financial backing to this deal."