Tangerines boss Jackie McNamara has made the 18-year-old his third signing from the Spiders following the capture of Andrew Robertson and Aidan Connolly a year ago.
Spittal has already played 59 games for Queen's Park and scored 13 goals in his 15 months with the League Two club.
McNamara said: "Blair was someone I was keen to bring to Dundee United so his signing delights me. He has versatility but it is his attacking threat which really caught my eye.
"It is of paramount importance that we continue to develop the younger players at Tannadice but we must also supplement that with other promising talent that becomes available.
"There were other clubs interested in Blair and it says everything about how we are developing players at Tannadice that he chose us as the best option for himself.
“Having watched his progress closely I am convinced that he will prove to be an excellent signing and entertain the United fans greatly."
Spittal said: "I spoke to Jackie and, although there were other options, I made up my mind quickly as this is where I feel I can continue to evolve as a footballer.
"Seeing how well Andy Robertson has progressed also played a part in my decision. Dundee United allow you to develop regardless of age and the manager's vision for the club excites me.
"I had a fantastic time at Queen's Park and will be forever grateful to them but I now want to focus on taking my game to the next level and when I look at the talent already in the dressing room at United I cannot wait to meet up with them and start my Dundee United career."