Scottish international Robertson has arrived for a fee of £2.85m while the deal to bring centre-half Maguire to the Tigers is worth £2.5m.
Both players have signed three-year deals, with the club holding an option to extend their stays by a further year.
The switch to the KC Stadium caps a remarkable rise for 20-year-old left-back Robertson, who was on a part-time contract with Queens Park in Scotland’s third tier at the end of the 2012-13 campaign before United spotted his potential.
He arrived at Tannadice in the summer of 2013 and last year was named as the PFA Scotland Young Player of the Year.
Robertson made his international debut for Scotland coming on as a second half substitute in a 1-0 win against Poland in March.
Maguire, 21, subject of several failed bids from Wolves earlier in the summer, has been named as the Blades’ player of the year in each of the last three campaigns.
Hull youngster Connor Townsend is heading to Dundee United on a season-long loan, as a direct replacement for Robertson.
Tigers target Carl Jenkinson is set to join West Ham on a season-long loan.