The Scotland internationalist will move to the KC Stadium for £3m, with the Barclays Premier League club having agreed to send Townsend in the other direction to serve as his replacement this season.
The 21-year-old left-back has still to make a senior appearance at Hull, for whom he signed a new 18-month contract in January, but is not without first-team experience, having spent time on loan at Grimsby Town, Chesterfield and Carlisle United. He is the sixth new signing at Tannadice this summer following the arrival of Callum Morris, Mario Bilate, Jaroslaw Fojut, Charlie Telfer and Blair Spittal.
The latter - who left Queen's Park this summer and signed a three-year contract at United - spent only a short amount of time training alongside Robertson this month, but is eager to follow in his footsteps on Tayside. The two players both found prominence at Queen's Park before signing for United; that move duly bringing Robertson to the attention of both Scotland manager Gordon Strachan and Hull's scouts. He is expected to sign a contract with the English club later today, with a fee agreed between the clubs last week.
It is something of a fairy tale for the left-back and one which has resonated with Spittal. The 18-year-old, a winger who has played as an auxiliary right-back during pre-season, is determined to make a name for himself at Tannadice too.
"It makes it easier for me after Andy made the same move as me from Queen's Park," said Spittal. "Seeing what he's done in the last year, if I manage half of that then I'd be over the moon. It inspires you, seeing what he's done - and hopefully it can happen again.
"He's the same boy he was at Queen's Park; he loves a laugh and stuff like that. He's not let any of it get to him, so that's a good thing. And I'm not going to get ahead of myself. I've got to work hard, because he never just walked straight into the team. He had to work hard and I know I'll have to do the same thing to get into the team. But having seen Andy do it before me gives me confidence that I can do it as well."
The habit United have picked up for developing talented youngsters into valuable first-team players will likely embolden him too. Spittal has witnessed former United youth Ryan Gauld agree a £3m move to Sporting Lisbon this summer as well, while Johnny Russell and David Goodwillie each earned transfers to England after rising through the ranks at Tannadice.
John Souttar, Stuart Armstrong, Keith Watson and Ryan Dow have all since broken into the first-team squad and played a prominent role for the club last season, while United were also quick to agreed extended contracts with the likes of teenage talents Scott Smith and Scott Fraser last season.
"I believe that's the reason why we've got the other lads coming in - the Charlie Telfers, Blair Spittals and guys like that," said Jackie McNamara, the United manager. "They see opportunities there."