Jim Fitton, 66, was jailed for 15 years after he was caught collecting 12 stones and shards of broken pottery as souvenirs.
Iraqi officials claimed the items could be considered archaeological pieces as they date back more than 200 years.
They arrested Mr Fitton after he visited a site in Eridu, in Iraq’s south east, as part of an organised geology and archaeology tour.
But Mr Fitton’s family say they are “over the moon” after being told he has now been cleared.
Undated handout photo of Jim Fitton, with his wife Sarijah Fitton and his daughter Leila Fitton Family handout
Son-in-law Sam Tasker, 27, from Bath, Somerset, said in a statement: “For the first time since March 20, Leila, Josh, Sarijah and I are smiling without irony.
“We were informed this morning that the appeals court has decided to quash the verdict of the Felony Court, to fully recognise Jim’s innocence in this case, and to process his immediate release from a 15-year prison sentence in Baghdad.
“We understand that this process is under way – he is still in prison this evening but will soon be released.
“We will not be doing any press interviews or elaborating at all about the situation until he is home, as we don’t want to inflame the wrong groups or put him at any risk.
“Once he is home, we will celebrate and take some time to recover as a family, and will be happy to tell the story to anyone who will listen.”
Jim Fitton, 66, was jailed for 15 years after he was caught collecting 12 stones Family handout
Wera Hobhouse, Liberal Democrat MP for Bath, welcomed the “fantastic development” and said: “It is impossible to imagine the stress that Jim and his family have endured over the past few months.
“Jim and his family have shown incredible strength and should be extremely proud of the role they have played in pressuring the Government to act. This has been an incredibly anxious time and the Government should consider how to improve the way they respond to these cases in the first instance.
“This is a testament to the hard work of the consulate team, Foreign Office officials and, of course, Jim’s family.”
A Foreign Office spokesman said: “We are providing consular assistance to a British national in Iraq, and continue to support his family. We are in contact with the local authorities.”