The new centre will be built in Knightswood on redundant red braes football pitches.
The city's executive committee also agreed almost £617,000 to extend mountain bike trails and facilities at Cathkin Braes Country Park.
Both locations will be venues for the Glasgow 2018 European Championships.
The new centre at Knightswood Recreation Ground will be the new home of the Western Titans BMX Club.
Riders of all ages and abilities will have a main track, while advanced riders will make use of eight and five metre start ramps.
There will also be a track for learners, and the tracks will be floodlit.
Plans include changing rooms, a meeting room, a car park and an access road from Archerhill Road.
Other funding for the centre is coming from the Glasgow 2018 European Championships, sportscotland and a partnership between HSBC bank and British Cycling.
Additional cash for the Cathkin Braes facility is coming from Glasgow City Council, sportscotland and LandTrust.
Work there will see the track brought up to international standards for the European Championships.
A new start-finish will be located closer to the local community in Castlemilk, with trails adapted to allow riders of all abilities to use them.
A Glasgow City Council spokesman said the funding was good news for local communities.
He said: "This funding will add to Glasgow's outstanding collection of sporting facilities, with these two fantastic venues open for the people of Glasgow and our visitors to use, and capable of hosting local, national and international events.
"There will be fantastic opportunities for local communities to take part in the development of cycling in Glasgow."
Work is to start on Scotland's first and only world and Olympic-standard BMX track after councillors in Glasgow agreed nearly £333,000 of funding.