Robinson had a turbulent two-year spell in charge of England which ended in November 2006.
But he insists his priorities will lie with Scotland if his new charges face England A at next summer's Churchill Cup.
He said: "I'm there to prepare a side to win a game and that's what I'll do. I'm a competitive person."
The role will be strictly part-time, with Scotland A having only two matches lined up in the next six months - they take on Italy A and Ireland A in February.
Scotland head coach Frank Hadden has lent his support to the duo.
"I'm delighted that two high-profile coaches are getting together," said Hadden.
"The development of potential Scotland players is something we take extremely seriously. I cannot think of two more appropriate guys to lead the progress of this exceedingly important team."
Robinson returned to the game on October 1 when the Scottish Rugby Union named him as the new coach of Edinburgh.
Several of the Murrayfield club's players will be involved at Scotland A level, and Robinson welcomed the opportunity to nurture the stars pressing for senior international selection.
"I'm honoured to be asked and I'm really looking forward to it," said the 43-year-old.
"I see it as building upon what I'm doing with Edinburgh. It's important for Scotland to have a strong A team."
Lineen believes he and Robinson can combine to good effect.
The 45-year-old said: "We need to ensure we have strength in depth and I look forward to working closely with Andy to build that."