Brendan Rodgers’ side cruised to victory in the semi-final at Hampden Park thanks to goals from Tom Rogic, Callum McGregor, Moussa Dembele and Olivier Ntcham.
Rangers had Ross McCrorie sent off when they were two goals down as they lost against their Glasgow neighbours for the eighth time in their last 10 meetings in all competitions.
Celtic, who have won the Scottish Cup 37 times, are chasing a domestic treble, having already beaten Motherwell in this season’s Scottish League Cup final.
The Scottish Premiership leaders are 37 points clear of Motherwell, who beat Aberdeen 3-0 in the other semi-final on Saturday.
Interim Rangers boss Graeme Murty was left to rue a damaging defeat that could ruin his chances of landing the Ibrox job on a permanent basis.
Murty had revealed Rangers players cheered when they heard they would play Celtic in the semi-finals, but that optimism quickly turned sour.
Rogic struck in the 22nd minute when he took a pass from James Forrest and turned back on to his right foot, leaving McCrorie for dead, before shooting past Rangers goalkeeper Wes Foderingham.
Rangers defender Russell Martin handed Celtic their second in the 38th minute.
Martin’s attempted clearance from Kieran Tierney’s cross went straight to McGregor, who quickly curled the ball past Foderingham.
Any thoughts of a comeback ended when McCrorie pulled back Dembele as he raced through on goal in the 52nd minute.
After McCrorie was given his marching orders, Dembele dinked his spot-kick down the middle for his seventh goal in nine Old Firm derbies.
Forrest bent a shot wide of the target before Rangers substitute Jason Holt conceded a penalty for a foul on Patrick Roberts in the 78th minute.
Ntcham despatched the spot-kick into the corner of the net to keep Celtic on course for a second successive treble.
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