They are expected to confirm that the debris was part of flight MH370, which disappeared off the face of the earth in March 2014 along with its 239 passengers and crew.
The British government has also pledged to help solve the MH370 mystery, with David Cameron offering a team of hydrology experts to his Malaysian counterpart over dinner earlier this week.
"Britain stands ready to aid Malaysia in their efforts to find this plane. We have offered our best analysts and scientists to help narrow down the search," Secretary of State Michael Fallon said in a statement on Friday.
The piece of plane debris is said to be a flaperon - a device used to regulate an aircraft's speed - and is a crucial clue that could unlock a riddle which has baffled investigators for more than a year.
A frenzied search was underway on Friday night as investigators combed the beaches of Reunion for other clues that might reveal what caused the plane to crash into the ocean.
But the discovery is bittersweet for anguished relatives of the missing passengers, with one woman admitting on Friday she had "selfishly" hoped the debris did not come from MH370.
Jennifer Chong, whose husband Chong Ling was travelling to Beijing on the flight, said: "My initial response was that 'this cannot be it' since we have had so many false leads before.
"Yet I cannot stop myself searching and scavenging for more information over the internet.
"I have waited 509 days to see Chong Ling again, alive. I selfishly hope this is not MH370," she added.
The debris, which featured the code "BB657" and allowed investigators to confirm it came from a Boeing 777 aircraft, was discovered by a gardener on Thursday morning.
Johnny Begue said he was looking for a stone to grind up some chillies when he came across a six-foot long object that had washed up on the shore.
"That was when I found the debris and realised from the roundness of it that it was from a plane," he said.
"There were screws and everything, I came down to look at it and called my friends who helped me" he added.
"To begin with we thought about taking it to use as a decoration, but then we thought about the families...we thought if this was a crash then there will be families of the people who died and we should respect them.
In a bizarre turn of events a large volcano on Reunion Island erupted within hours of the discovery, prompting speculation the search could be disrupted by ash clouds.
But Australian officials said the volcano, located in the south-eastern corner of the island, was unlikely to have an impact on their investigation.
There was also speculation that two plastic bottles that washed up on the beach with Chinese and Indonesian writing on them came from flight MH370.
A French newspaper has already poured cold water the theory, pointing out they could just as easily have come from Asian cargo ships that cruise nearby.
