The draw was made at Hampden on Sunday evening following Aberdeen's 1-0 quarter-final win over Partick Thistle at Pittodrie.
Celtic sealed their spot by coming from behind to beat St Mirren 4-1 earlier in the day.
On Saturday, Rangers beat Hamilton 6-0 and Hibs saw off Ayr United 3-1.
The semi-final ties will be played on April 22/23.
Aberdeen manager Derek McInnes expects a tough match against Neil Lennon's Hibs, but admitted to a slight sense of relief over the draw.
"If we are all being honest, Celtic are the strongest team by a long way," he told BBC Radio Scotland.
"So it is a good draw and Hibs will probably see it as a good draw.
"Hibs have done really well and are holders and this is the type of game you want to be involved in.
"If you look at the level of player Hibs have got, the experience of the manager and the fact they won the cup last year and have that experience, there shouldn't be too much between the teams.
"If we are deemed to be favourites, so be it and we just have to do our business on the pitch."
Celtic and Rangers meet in the league on Sunday, with Brendan Rodgers' team having won the three matches between the sides so far this season.
They followed a 5-1 win at Celtic Park with a 1-0 League Cup semi-final win and a 2-1 Premiership victory at Ibrox.
Hibs beat Rangers 3-2 in last season's final to lift the Scottish Cup for the first time in 114 years.
They have played Aberdeen 32 times in the Scottish Cup, winning nine times, losing 13 times with 10 matches ending in draws.

The poll has been triggered by the resignation of Tory MP Zac Goldsmith in protest at the government's backing for a third runway at Heathrow.
Mr Goldsmith, who will run again as an independent, has said it "must be a referendum on Heathrow expansion".
But the likely Lib Dem candidate said Mr Goldsmith's backing for Brexit would be "uppermost in voters' minds".
Sarah Olney, who has already been selected to fight the seat at the next General Election, said it was a "farce" the by-election was taking place, saying it was the result of Tory in-fighting but added that the Lib Dems were looking forward to "putting our message in front of voters".
Ms Olney, who like Mr Goldsmith is opposed to Heathrow expansion, told the BBC's Daily Politics: "We are on the same side as far as Heathrow is concerned, so for the voters to be able to choose between us, it's going to be fought on other issues - and I think Brexit is currently going to be the main issue that's uppermost in voters' minds."
A local breakdown of the EU referendum results shows almost 70% of voters in the Richmond council area, which makes up the bulk of the constituency, backed Remain.
Ms Olney is expected to be confirmed as the party's pick for the by-election after party leader Tim Farron rejected the idea of parachuting in one of its big names.
The Conservatives are not fielding a candidate against Mr Goldsmith, who held the south-west London seat in 2015 with a 23,015 majority. The Lib Dems, who held the seat until 2010, finished second.
Labour says it will field a candidate despite three of its MPs urging it to consider standing aside to maximise the chances of a Tory defeat.
The Green Party said it was also likely to put forward a candidate although it said it supported "progressives working together to beat the Conservatives".
In standing down, Mr Goldsmith - who has long campaigned against a third runway -  fulfilled a pledge to quit if the government backed the expansion.
He said: "There was no small print, no expiry date, no ambiguity. It was a simple promise. And it mattered.
"I know it mattered, because the thought of Heathrow expansion fills most of my constituents with dread."
Celtic and Rangers will meet in the Scottish Cup semi-final at Hampden, while holders Hibernian face Aberdeen in the other last four match.
[NEXT_CONCEPT]
The Liberal Democrats have vowed to make the Richmond Park by-election about Brexit, not Heathrow.