The 50-year-old will take up a new role as head of player acquisition and manager of the national Under-20 side – a role which is understood to involve setting up a worldwide scouting network for the SRU – as his six-year stint as Glasgow head coach comes to an end.
Lineen will be replaced by Gregor Townsend, whose role as Scotland attack coach has come under huge scrutiny during a horrendous Six Nations campaign for Andy Robinson's men.
The Scots were hammered by Ireland on Saturday, going down 32-14 at the Aviva Stadium, to rack up their fourth defeat in the championship this year and their sixth in a row dating back to last year's competition.
Despite has appointment to step into Lineen's shoes, Town-send has no experience of coaching at club level.
And the timing of the move by the SRU seems bizarre, given that Lineen's latest talented batch of young players, including Duncan Weir and Stuart Hogg (both of whom have just been capped at full international level), appear to be maturing into a fine team.
Lineen's big-name recruitment drive, meanwhile, has brought Scotland internationalist Rory Lamont to Firhill, with his brother Sean set to arrive in the summer along with Tongan star Viliami Ma'afu.
Warriors already have a far better depth to their squad than in recent years, despite a succession of star players making lucrative moves elsewhere, while they have lifted the 1872 Cup for the last three years.
Glasgow currently sit in the fourth and final Pro12 play-off place and are set to host Italian backmarkers Aironi on Friday night at Firhill.
However, it will be Townsend who oversees their future and it is believed that Scotland's defence coach, Matt Taylor, will assist Townsend, which may mean Gary Mercer, Glasgow's present equivalent, could also be moving on.
Lineen's assistant Shade Munro is, though, expected to continue as forwards coach
In any case, the New Zealand-born Scot has vowed to go out on a high. He said: "I have a good run here of nine years overall, with six of these as head coach, which is a fair old crack of the whip by any standard.
"What is important now is that this does not distract us from the remainder of the season and nailing down a play-off place for the second time in three seasons.
"We have a massive home game with Aironi coming up on Friday and it is vital that every one of the fans gets along and supports the guys to a victory. I am determined to go out on a high and that means booking a play-off berth and hopefully even better."
Reflecting on his time in charge, Lineen admitted there have been plenty of high points.
He said: "Obviously it has been great to oversee the move to Scotstoun and, on the playing front, we have had some great wins in Europe, with probably the victory over Toulouse in France the best of those.
"But I have just loved working with the players and we have got an exciting new group coming through at Glasgow and hopefully they will finish this season on a high and then kick on."
lEngland secured a superb 24-22 win over France in a nailbiting Six Nations encounter in Paris yesterday.