The centre-back has finally joined the Premier League outfit following an initial breakdown in negotiations with Sheffield United as the left-back arrives from Dundee United
Both players have joined on three-year deals, with centre-back Maguire arriving from League One oufit Sheffield United and left-back Robertson from Scottish Premiership side Dundee United.
The signing of Maguire puts an end to the confusion over the 21-year-old's future following an apparent breakdown in communication between Hull and Sheffield United.
On Monday, Sheffield United claimed to have "reluctantly accepted" a bid for Maguire, only for the Premier League club to then state that they had moved on to other targets after having a "final offer" rejected by their Yorkshire counterparts.
But the matter has now been settled, allowing Maguire to make the step up to the English top flight in a deal worth £2.5 million.
Meanwhile, 20-year-old Robertson has been signed for £2.85million following an impressive spell at Dundee United.
Robertson moved to Tannadice in June last year, going on to score five goals in 44 appearances and win the PFA Scotland Young Player of the Year award.
The Glasgow-born full-back made his international debut for Scotland against Poland in March.
Hull's Conor Townsend has gone in the opposite direction to Robertson, moving to Dundee United on a season-long loan deal.