During a news conference, a video was shown of a purported confession from Mr Hedges, saying he was a member of MI6.
This accusation was rejected by Ms Tejada, who told BBC Radio 4s Today programme: "Its taken me by surprise and Im just so happy and so relieved and really incredulous that it is all happening finally.
"Its been an absolutely nightmarish seven months already and I cant wait to have him back home."
Foreign Secretary Jeremy Hunt said the UK government had "never seen any evidence" the spying charges were true.
He praised Ms Tejada, describing her as a "determined lady" who had "fought incredibly hard and been to hell and back".