A skeleton of a meat-eating Jurassic dinosaur, the theropod, was uncovered by spring storms at Lavernock beach, Vale of Glamorgan, in 2014.
The dinosaur's missing foot was found at the beach by palaeontology student, Sam Davies, of Bridgend, at the beginning of this month.
"My first reaction was that I was very lucky," he said.
The fossilised skeleton of the theropod - a distant cousin of the giant Tyrannosaurus rex - went on display at the National Museum Cardiff's main hall in June after it was found by fossil-hunting brothers Nick and Rob Hanigan.
Mr Davies, who studies at the University of Portsmouth, visited Lavernock, near Penarth, after his tutor told him its cliffs were rich with fossils.
He arrived only hours after a cliff fall had exposed the fossil and before it could be washed away by the tide.
"It was pure luck that I found it. It was just sitting on top of a slab of rock," he said.
His tutor, Dr David Martill, confirmed the find was the missing foot of the recently discovered dinosaur, after the student emailed a picture.
Dr Martill said: "This was a chance-in-a-million find and highlights how important it is to encourage fossil hunting in this country."
He said the specimen would help chart the evolution of dinosaur feet.
The foot has been donated to the Amgueddfa Cymru, which hopes to put it on display with the rest of the skeleton soon.
Dr Caroline Buttler, head of palaeontology at the museum, said: "The dinosaur found by Nick and Rob Hanigan is the first skeleton of a theropod found in Wales.
"Sam's find adds to its significance because we can learn more about the animal and how it is related to the dinosaurs that eventually evolved into birds."

Under the rules, racegoers will also have to wear skirts or dresses of "modest length" falling just above the knee or longer.
For men, a waistcoat and tie will be compulsory in the enclosure and cravats will not be allowed.
Organisers said the decision was part of a move to restore formality.
The annual week-long event in June attracts about 300,000 visitors each year.
The popularity for elaborate fascinators, which are a cross between a hair accessory and a mini hat, continued last year after the Duchess of Cambridge wore a feathered one on her first official engagement in Anglesey.
In the less formal grandstand, which is open to the public, it will now be compulsory for women to wear a hat or fascinator.
In previous years, when female racegoers were simply advised that "many ladies wear hats".
Strapless or sheer-strap tops and dresses will also be banned.
For men, a suit and tie will now be obligatory.
Ascot spokesman Nick Smith said: "It is probably fair to say the dress code hasn't necessarily been enforced quite as rigorously as we might have liked.
"There is no doubt our customers would like to get back to a situation where it is universally acknowledged this is a formal occasion and not an occasion where you might dress as you would at a nightclub."
Charles Barnett, Ascot's chief executive, said the intention was to be "as helpful as possible" to visitors and to help racegoers in understanding what is "cherished" about the dress code at Royal Ascot.
"It isn't a question of elitism and not being modern in a world where there is less and less requirement to dress smartly - far from it," he said.
"We want to see modern and stylish dress at Royal Ascot, just within the parameters of formal wear."
The less formal Silver Ring will not be affected by the changes.

The deal, which is worth about £97m, was confirmed at the SNP's annual conference in Aberdeen by Transport Minister Derek McKay.
Ferguson's had previously been named as the preferred bidder for the contract.
The firm was saved by businessman Jim McColl's Clyde Blowers Capital after it went bust on 15 August. Mr McColl is one of Scotland's wealthiest people.
Originally formed in 1902, Ferguson's employed 77 staff at the time of the administration appointments.
The fossilised foot of a dinosaur has been discovered on a south Wales beach, National Museum Wales has announced.
[NEXT_CONCEPT]
Women will have to wear hats, not fascinators, as part of a tightening of the dress code in Royal Ascot's Royal Enclosure this summer.
[NEXT_CONCEPT]
Ferguson's shipyard on the Clyde has won a Scottish government contract to build two new ferries.