Mel Parry was part of the SAS team which ended the 1980 siege after six armed men took 26 people hostage within the building.
The hostage takers were Iranian-Arabs campaigning for the sovereignty of Khuzestan, a province in the south west of the country.
They demanded the release of prisoners held in Iran, as well as their own safe passage out of the UK.
In one of the elite unit’s most famous operations, the SAS soldiers stormed the embassy in 17 minutes on day six of the siege.
They rescued all but one of the hostages, killing five of the six hostage takers in the process.
Mr Parry’s former SAS colleague Bob Shepherd paid tribute to him in his blog.
“It’s with the greatest of sadness that I write this blog post about arguably one of the finest men to have served in 22 SAS Regiment in my time,” he wrote.
“I write this as he died from a very long illness today in Hereford. My heart goes out to Mel’s family and close friends.
Another former SAS soldier, Chris Ryan, paid tribute to Mr Parry on Twitter.
“Mal, you were a gentleman and an incredible soldier,” he tweeted.
“We first met when I joined B Squadron in the early 80s and you were the guiding light of the CT [Counter-Terrorism] world that we recognise today.
“God Speed and don’t spare the HE [High-Explosive].”
An Army spokesperson said: “We are saddened to hear of the passing of Mel Parry who had a long and distinguished career.
“We are thankful for his service, dedication, excellence and enduring legacy.
“Our thoughts are with his friends and family.”
