"I think what you've told me is by far the strangest, most incredible story that I have been told about someone watching me. Nothing has come close to that, so that's incredible...speaking to you I'll certainly make sure I'm a lot more grateful for everything that I've got" - Murray
Zaghari-Ratcliffe was imprisoned in Iran for six years until her release earlier this year, having been accused of spying, a charge she and the UK denied.
She was asked to guest edit a BBC Radio 4's Today programme during the festive period and Murray was one of her guests with the episode broadcast on Wednesday.
Zaghari-Ratcliffe recalled how she was given access to a TV with two channels in 2016 and matches at that year's Wimbledon were shown with Murray triumphing at the All England Club after he beat Milos Raonic in the final.
"I think what you've told me is by far the strangest, most incredible story that I have been told about someone watching me. Nothing has come close to that, so that's incredible," Murray told BBC Radio 4's Today programme.
Zaghari-Ratcliffe revealed watching Murray's victory was "joyful" and made her "ecstatic" a couple of months on from her initially being detained in Iran.She later explained how at the time she hoped to watch the former world No 1 in person at Wimbledon at the next Championships in 2017, only to spend a further five years in prison.
The 44-year-old British-Iranian dual national said Murray offered a "connection" to her life outside prison and an "escape" from her six-year detention.
Murray's voice cracked with emotion and he paused to gather himself when they met at the Lawn Tennis Association in Roehampton for her stint as guest editor of BBC Radio 4's Today programme.
Zaghari-Ratcliffe, who was freed in March, used the programme to raise the plight of others suffering at the hands of the Iranian regime, amid widespread protests in the country.
In her interview with Murray, Zaghari-Ratcliffe said: "When I was first arrested I was in Evin prison in solitary confinement, and for about five months they didn't allow me to have any books or newspapers.