The bridge was the result of a competition launched in 1996 by the Millennium Bridge Trust and promoted by the Financial Times, Royal Institute of British Architects and Southwark Council.
The design, which avoided blocking the view of St Paul's with tall suspension towers, was a partnership between architectural firm Foster + Partners, the late sculptor Sir Anthony Caro and engineers Arup.
The concept of the bridge as a "blade of light" was designed by Lord Foster, and early sketches were drawn on the back of a napkin in a central London wine bar by engineers Chris Wise and Roger Ridsdill Smith.
"We spent hours in there, sketching and sketching and trying to come up with an idea," Mr Wise said.
"We got more and more minimal until it was one line connecting the river from side to side.
"I was on the bridge on opening day with my son on my shoulders when it started to wobble. I did feel very responsible, but I don't recall any sense of crisis – it was more fascination, what's the problem and what can we do about it?
"It's great to have been involved in something that's now part of the fabric of London."