He has said the treaty could turn the EU into a super state with little democratic control.
Klaus sought an opt-out from the treaty nearly three weeks ago, after Prague's parliament ratified it, in an attempt to ensure the treaty would not allow ethnic Germans expelled from former Czechoslovakia after the second world war to reclaim their property.
Al Jazeera's Hamish Macdonald, reporting from London, said the Czech endorsement is a "significant" development for the EU.
"It's going to pave the way for some pretty enormous changes," he said.
"Perhaps the most high-profile of which will mean there will now be an EU president, a figurehead that is effectively the chairman of the EU council.
"It will also give the European Union a senior foreign policy position, if you like a foreign minister, that will deal with things like Iran and the nuclear debate, Russia and also Afghanistan."
The EU president, who needs to be elected unanimously, will serve a two-and-a-half-year term, strengthening the current system of a six-month presidency that states hold in turn.