Its exact location is yet to be confirmed but the preferred options are close to the site of the new US Embassy.
The bridge is part of a £2bn infrastructure package transforming Nine Elms into a new Zone One transport hub complete with two new Northern Line tube stops.
Ravi Govindia, leader of Wandsworth Council and co-chair of the Nine Elms Vauxhall Partnership, said: “This will be a new bridge at the centre of the world’s greatest city so the design standard has to be exceptional.
“It will be a dream commission for the winning architect but to succeed they will have to meet some very unique challenges and expectations.
“The design will have to inspire and win the hearts of Londoners who are tremendously proud of their river and its heritage.
“It must work alongside the cutting edge modern architecture of Nine Elms as well as the elegant buildings on the north bank.
“There will be engineering feats to overcome and the landing points on both sides must integrate sensitively and effectively with their surroundings.”
Once a design is in place Wandsworth Council will explore further funding options including sponsorship.
Plans for the competition will now be finalised and the official launch could take place in winter 2014.
A shortlist would be selected in early 2015 and the winning design announced in spring the same year.