Scotland finished the Six Nations with the wooden spoon, leaving Robinson to consider his future despite being under contract until the 2015 Rugby World Cup.
A statement from the SRU read: "(SRU chief executive) Mark Dodson and Andy Robinson met on Thursday for discussions following the RBS 6 Nations.
"The discussions were positive and concluded that Andy will continue to lead the Scotland national team with the support of his revised coaching structure."
Robinson entered a period of introspection after a Six Nations campaign which ended with a 13-6 loss to Italy in Rome on March 17. The defeat was Scotland's 12th in 15 Six Nations matches under Robinson.
It was also Scotland's seventh successive defeat - the worst sequence of results since 1998 - following the failure to advance from the World Cup group stages for the first time in New Zealand. Scotland's last Test win was the September 14 defeat of Georgia in Invercargill.
Following the loss to Italy, Robinson was adamant the decision over whether he would stay remained his.
He said: "I'm still contracted until 2015. I'm going away to reflect on the Six Nations and reflect on the future, in terms of the positivity that we have, the players we have and the way forward - and putting a plan together for the way forward.
"There's a lot to take in in terms of what's happened and it's about looking at the future and what's best for the future."
Robinson was encouraged by the performances of young talent such as Edinburgh number eight David Denton and Glasgow Warriors full-back Stuart Hogg, both of whom made their first Test starts during the Six Nations, and has now been convinced to stay.
Robinson will now conduct a review of the tournament before leading Scotland on the summer tour of Australia, Samoa and Fiji, with new support staff in place.
Robinson recruited Scott Johnson as senior assistant coach and Matt Taylor as defence coach, with Gregor Townsend and Graham Steadman - formerly attack and defence coach, respectively - departing. Townsend is next season set to replace Sean Lineen as Glasgow Warriors head coach, with Taylor his assistant.
Many of Scotland's problems were self-inflicted, with individual errors, indiscipline and lapses in concentration contributing to the losing streak.
Prior to the Six Nations, former Bath and England flanker Robinson described his tournament record with Scotland as "unacceptable" and the campaign began promisingly.
Scotland appeared close to producing a positive result in the losses to England, Wales and France, but the displays against Ireland and Italy were disappointing.
Robinson, who has a record of 12 wins in 29 matches as Scotland head coach, has revolutionised Scotland's style of play but it is yet to yield results.
However, in the likes of Richie Gray - a British and Irish Lions second row in waiting - flanker Ross Rennie, wing Lee Jones, Denton and Hogg, Robinson recognises the potential is present for a bright future.