The two legs of the quarter-finals will be on 9 and 12 May with the semi-finals held over 16 and 19 May.
The first leg of the final will be on 25 May, with the second leg on 28 May.
Falkirk or Dundee United - currently second and third in the Championship - will play Greenock Morton in the quarter-final.
The side who finishes higher in the league will bypass the quarter-finals and meet that tie's winner in the semi-finals.
The final round of Championship fixtures takes place on Saturday, with Falkirk away to Dumbarton and United visiting Morton. The Bairns are currently one point ahead of the Tangerines.
The semi-final winners face the Premiership's second bottom side in the final and the winner will be in the top flight next season, the loser consigned to the Championship.
All of the Premiership's bottom six clubs - Kilmarnock, Ross County, Dundee, Hamilton Academical, Motherwell and Inverness Caledonian Thistle - are in contention to occupy the second bottom place, with the side finishing 12th being relegated automatically.
There are four rounds of Premiership fixtures remaining and Killie are the only one of the bottom six sides that will definitely avoid finishing in bottom place.
Championship winners Hibernian have already secured promotion to next season's Premiership, while Morton can finish no higher than fourth.
To ensure Dundee's home match against Inverness does not take place on the same night as a Dundee United home match in the play-offs, Dundee v Inverness has been moved to 17 May.
Quarter-final
9 May: Morton v Championship third-placed side
12 May: Championship third-placed side v Morton
Semi-final
16 May: Quarter-final winner v Championship second-placed side
19 May: Championship second-placed side v quarter-final winner
Final
25 May: Semi-final winner v Premiership 11th-placed side
28 May: Premiership 11th-placed side v semi-final winner
The Scottish Professional Football League has announced dates for the Premiership play-off quarter-finals, semi-finals and final.