They will also face Montpellier, now coached by former Scotland team boss Vern Cotter, and Leinster, who were second in the Pro12 table last season.
Montpellier finished third in the French Top 14.
The first pool match will be on either 12/13/14/15 October, with the final on Saturday 12 May in Bilbao.
Glasgow reached the quarter-finals for the first time last season after home and away victories over both two-time European champions Leicester and French giants Racing 92 in the pool stages.
The Warriors finished runners-up to group winners Munster, and were beaten by eventual champions Saracens in the last eight.
Glasgow beat Montpellier home (21-10) and away (15-13) when they met in the pool stages of the 2014-15 Champions Cup, and also overcame Exeter twice in their group the previous season, winning 20-14 at home and 15-10 at Sandy Park.
Leinster are familiar foes in the Pro12, with Warriors beating the Irish province 33-25 at home last season, before losing 31-30 at the RDS in Dublin in late April.
The last time they met in Europe in 2011-12, Leinster prevailed home and away to finish top of the group on route to their third European title in four seasons.
Glasgow were distant runners-up, having also beaten Montpellier at home and drawn away in the same campaign.
Glasgow's new forwards coach Jonathan Humphreys, who worked alongside Cotter with Scotland before moving to the Warriors this summer, said he had a sense of inevitability about the draw.
"We talked to Vern about this a fair bit during the Six Nations - we were convinced it was going to happen!" he told the Warriors website.
"We've worked together for a long time, so we know what the strengths and the style of play of Montpellier will be, although we said we would double-bluff each other.
"It's a really exciting group and we're looking forward to it. Leinster, Exeter and Montpellier all want to play a good brand of rugby."
Glasgow Warriors have been drawn against English Premiership champions Exeter Chiefs in their four-strong European Champions Cup pool.