Robinson, 45, leaves his role as head coach of Edinburgh, where he has been in charge for almost two seasons.
He will be tasked with reviving Scotland's dwindling fortunes, with Hadden having managed just one Six Nations win in each of the last three championships.
Robinson has been given time to achieve that aim after signing a three-year contract.
Speaking at a press conference at Murrayfield this afternoon, Robinson said: "I'm deligthed and honoured to be appointed head coach of Scotland.
"I've worked in Scotland now for 18 months and I've been really impressed by the attitude and potential of Scotland's rugby players.
"I'm now looking forward to developing that attitude and potential into winning performances."
As well as working with many current Scotland internationals at Edinburgh, Robinson has been involved in the national team set-up for some time.
He was an assistant to Hadden during last summer's tour to Argentina and has taken charge of the A team on more than one occasision.
Indeed, he will lead the squad during the IRB Nations Cup in Romania, which begins next week.
The Scottish Rugby Union were keen to have a new man in place ahead of that three-match tour.
Robinson was one of a number of candidates interviewed by a five-man SRU panel, which included former Scotland and Lions stars Andy Irvine, Andy Nicol and Gordon Bulloch.
SRU chief executive Gordon McKie and chairman Alan Munro were also on the panel.
Since taking over at Edinburgh in 2007, Robinson has twice led them to their highest-ever Magners League finish: fourth last season and second this year.