A 5-1 win at Kilmarnock, which featured a Kyle Lafferty hat-trick, ensured Rangers finished a point ahead of bitter Glasgow rivals Celtic whose 4-0 win over Motherwell proved academic.
Smith, 63, will be replaced in the Ibrox hotseat by his assistant Ally McCoist.
Smith's two spells in charge of Rangers yielded 10 titles, including seven consecutive championships in the 1990s.
He also managed Scotland between 2004 and 2007 and had a four-year spell in charge of Everton in the Premier League.
"It's fantastic, we deserved to win the title," Smith told Sky Sports. "I set the players a challenge not to lose any of our last 10 games (after losing at home to Dundee United on April 2) and they responded."
It was a bitter league finale for Celtic manager Neil Lennon, who was attacked by a man during his team's match against Hearts in Edinburgh on Wednesday.
The incident was the latest in a succession of problems for the former Northern Ireland and Celtic captain Lennon, who has received death threats on several occasions and retired from international football because of them.
Last month parcel bombs sent to Lennon and two high-profile Celtic supporters were intercepted.
The acrimony between Celtic, who have a predominantly Catholic fan base and Rangers, whose supporters are mainly Protestant, is long-running and deep-seated.
Lennon and Celtic can still end the season with some silverware if they beat Motherwell in next weekend's Scottish Cup Final.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
