UEFA President Aleksander Ceferin announced on Thursday that England's national stadium would now host the three group stage games and one knockout match slated for the proposed new "Eurostadium" in Belgium.
But the exclusion of Brussels means the 90,000-seater venue will also get group games and a match in the first knockout round.
To celebrate the 60th anniversary of the tournament, Euro 2020 is to be played in 12 cities across Europe, with cities divided into pairs and each pair sharing matches in a particular group. "If the answer had been no, it would have been a problem for us to find a new stadium".
UEFA also picked Rome to stage the opening game of the 24-team competition.
However they said UEFA's decision "does not necessarily signify the end of the stadium project".
Khan said: "It speaks volumes about our great city that London has been awarded an additional four Euro 2020 matches, reinforcing the capital's reputation as the sporting capital of the world".
It said that Group A would be played in Rome and Baku, Group B in St Petersburg and Copenhagen, Group C in Amsterdam and Bucharest, Group D in London and Glasgow, Group E in Bilbao and Dublin and Group F in Munich and Budapest.
Here's where the group-stage matches will be played.
UEFA has previously indicated that qualified nations that are home to one of the 12 host cities would be assigned to that group - meaning Spain and Ireland would be automatically paired up.
'The concept of taking Euro 2020 to 13 different countries was devised to allow smaller countries, like Wales, to have a unique opportunity of being involved in staging a major tournament.
'UEFA ranked the Champions League final as one of their best events and praised the way in which the Cardiff 2017 local organising committee delivered the showpiece.