The challenge took six months, 11 days, seven hours and 53 minutes to complete.
"This is a phenomenal achievement the magnitude of which will only come to light as Richard begins to tell the story of his adventures," said WRU chairman David Pickering, who has himself climbed Mount Kilimanjaro, just one of Parks' seven summits, as part of his fundraising work for NSPCC.
"Richard has taken the desire, determination and mental strength that made him a top sportsman and channelled that energy into pulling off an amazing feat of human endurance and endeavour in the name of an extremely deserving charity.
"Welsh rugby and, I'm sure, the rest of Wales is extremely proud of him."
Flanker Parks, who was born in Newport and represented his country twice in the 2003 RBS 6 Nations as well as featuring against both South Africa and Fiji, played his Welsh Regional rugby at Celtic Warriors and the Dragons.
He retired from the sport with a shoulder injury in 2009 and embarked upon his epic journey, which aims to raise £1million for Marie Curie Cancer, on 12th December 2010.
"Congratulations to Richard, a remarkable man and an amazing achievement Welsh rugby is proud to call you one of its sons," said WRU chief executive Roger Lewis.
"We have been keenly following Richard's progress since the very start when he announced his mission to raise this money for charity in Cardiff Bay and we have been equally proud that he has carried Welsh rugby's three feathers on his kit for the duration of his journey.
"Richard is a special person, he has taken Wales to the world and the world has been forced to sit up and take notice and he is a credit to us all."
Parks fell seven metres into a crevasse on Denali in Alaska and has had to overcome frostbite on his right big toe to achieve his 737 Challenge.
He also reached the North and South Poles and climbed the summits of Kilimanjaro and Mount Everest as part of the charity challenge.
"To stand on the top of the world's highest mountains and some of the most beautiful places on earth, I'm just so grateful to so many people who've made the 737 Challenge possible" he said.