Scottish international Robertson arrives for a fee of £2.85m whilst the deal to bring Maguire to the Tigers is worth £2.5m.
Both players have put pen-to-paper on 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.
At the end of the 2012/13 campaign, he was on a part-time contract with Queens Park in Scotland’s third tier before Dundee United spotted his potential.
He arrived at Tannadice in the summer of 2013 where he quickly earned a reputation as one of Scottish football's brightest prospects.
In his first season as a Dundee United player, Robertson made 44 appearances in all competitions, scoring five goals. His impressive performances saw him named the PFA Scotland Young Player of the Year as well as also being selected in the PFA Scotland Team of the Year for the 2013/14 Scottish Premiership.
He made his international debut for Scotland coming on as a second half substitute in a 1-0 win against Poland in March 2014, before being handed his first start in a 2-2 draw with Nigeria in May.
Maguire meanwhile has been a stalwart of the Sheffield United defence for the past three seasons having progressed through the youth ranks at Bramall Lane.
He made his debut at the back end of the 2010/11 campaign against Cardiff City and quickly cemented his place in the first team.
His performances and consistency at the back in a Sheffield United shirt saw him named as the Blades’ Player of the Year in each of the last three campaigns, whilst last season also saw the highly-rated 21-year-old pick up the club’s Players' Player of the Year, Supporters’ Player of the Year and The Sheffield Star's Player of the Year awards.
In total, Maguire made 166 appearances in all competitions as a Sheffield United player, scoring 12 goals and has also been capped once at England Under-21 level, coming on as a second half substitute in a 2-0 win against Northern Ireland in November 2012.