The proposed investment would include the development of a regional track cycling facility and closed 1km road loop circuit at Hunters Hall Park, the home of the Jack Kane Sports Centre.
Additional facilities, such as a BMX track, may be added later.
The move follows discussions with governing bodies and the cycling community regarding their desire to see improved cycling facilities in the city.
The commitment is part of the Council's £1.215m investment in sports facilities, which will also include the addition of a new 3G pitch at the Jack Kane.
Council officers will submit applications to sportscotland and other bodies with a view to securing additional funding.
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Cllr Richard Lewis, Culture & Sport Convener, City of Edinburgh Council, said: "In line with our Capital Coalition pledge, we are committing substantial funding towards improving Edinburgh's sporting infrastructure, particularly in relation to cycling.
"The phenomenal success enjoyed by Sir Chris Hoy has acted as an inspiration to many and interest in cycling is at all time high. We have already allocated 6% of our transport budget to cycling improvements across the city but, through this investment, we want to encourage and support competitive cycling as well.
"While these plans are at a very early stage, our vision is to create a cycling hub which will be accessible all year round by cyclists of all ages and abilities.
"This is an investment in Edinburgh's sporting future but also in the continued regeneration of Craigmillar."
Sir Chris Hoy today welcomed the news: "I'm delighted to hear that a new velodrome and road circuit are being built in my home city of Edinburgh, and very pleased to hear that the council is investing in local sports facilities and in cycling in particular, to provide decent access and facilities for people wanting to get in to the sport.
"This is great news for Edinburgh and for the future of Scottish sport."
The detailed plans, costings and timescales for the new facilities will be developed in partnership with partners and stakeholders.
(GK)
