The Scottish League Cup third round draw has produced two top-flight ties with Motherwell hosting Hibernian and St Mirren visiting St Johnstone.
Celtic travel to face Ross County, who defeated Neil Lennon's side in the Scottish Cup semi-final in 2010.
Kilmarnock will host Queen of the South, holders Rangers travel to Falkirk, while Hearts journey to Ayr and Airdrie take on Dundee United.
Second Division East Fife make the trip to Pittodrie to play Aberdeen.
Celtic defender Charlie Mulgrew is looking forward to facing County but does not think the Scottish Cup final defeat to County - or previous upsets involving Highland neighbours Inverness Caledonian Thistle - will be a factor.
"It's a good game for us, especially after the Scottish Cup semi-final a couple of years ago," he told BBC Scotland.
"It is a tough game but one we will look forward to.
"We will just be approaching it like any other game."
County director of football George Adams realised it would take a major effort for his side to repeat the 2-0 win over Celtic.
"It gives us encouragement, but there is a reality here - Celtic are a top, top team and we realise that we would need to be at our very best to look to have a chance of proceeding in the competition," he said.
"We are delighted to get a home draw - that's is the most important thing.
"It brings back good memories for the football club, so it will be a great day out for everybody."
As well as reaching the Scottish Cup final, County have won the Challenge Cup so have a good recent knock-out pedigree.
"Over the years, we have been known as a cup team and obviously, with a vociferous home support, that will make a big difference to us," added Adams.
"I think financially it might have been better to have been at Celtic Park. But, from our fans point of view, it will be great for them to see Celtic on our own ground."
The Scottish Communities League Cup third round draw:
St Johnstone v St Mirren
Ross County v Celtic
Kilmarnock v Queen of the South
Falkirk v Rangers
Motherwell v Hibernian
Ayr United v Heart of Midlothian
Aberdeen v East Fife
Airdrie United v Dundee United