Udeze, who spent the better part of his career in Greece playing for Kavala, PAOK Salonika, and AEK Athens, believes that the move will allow the forward time to settle down, away from the spotlight, to play regular football.
"Him going to Greece is a good one because it is a very good place for him to relaunch his career," Udeze told ESPN.
"He will get more playing time at Olympiakos and also has the chance of playing in the Champions League or Europa League once again."
In his final season in Belgium, he scored 22 goals, a tally which caught the eye of giants Paris St Germain and he was all set to join the French megaclub after completing a medical, before opting instead for Everton.
Work permit issues meant he could not make an appearance for the Toffees and he was immediately farmed out on loan to Anderlecht.
Six more moves have followed in the four years since, including a successful spell on loan in Turkey with Galatasaray which led to a permanent transfer to Monaco in 2019.
But Onyekuru made just eight appearances for the Ligue 1 club in his three years there, as he struggled to settle down, returning twice on loan to Galatasaray where he became a cult figure.
So much so that the Turkish club wanted him on a permanent basis, only to be priced out of a move by Olympiakos, according to coach Fatih Terim.
Terim said, as quoted by Sporx: "For Onyekuru, according to our option, we were asked for fifty percent of his buyout. That is 4.375 million Euros.
"To get him outright we would have had to spend double that amount, and yet he goes to Olympiakos for 5 million.
"We also wanted him at Galatasaray, but sometimes it just doesn't happen. We have to accept that it is the nature of football transfers.
"The previous management also wanted to buy him from Monaco but it was in the middle of an administrative change, so I can understand the challenges."
Udeze admits that Greece may be a bit of a backward step for the forward, but insists that it is a good way for him to push the rest button on his career.
He added: "He is a very young player. Him signing three or four years for Olympiakos does not mean he will stay there for the entire time.
"It is just for him to settle down and use it to reset his career. I think it is a good one for him going there.
"As a player, it is really difficult to get your head in the right place when you are going on loan season after season. Your mind will not be settled.
"For Henry, all he needs to do now is think about playing football, nothing else. What he needs now is full time concentration to play week in, week out.
"From there anything can happen in the near future, he is a young player and he still has a lot of time to play football."
It is a sentiment that Onyekuru agrees with, telling the media after his latest signing: "I have moved a lot in the last few years and I definitely need stability for a longer time.
"I have joined the biggest team in Greece, competing regularly in the European Champions League and targeting major titles, so the plan is to make a big contribution and win trophies here.
"I had interest from elsewhere, but I wanted to challenge myself all over again and Olympiakos gives me that opportunity."
Unfortunately for him, this season's Champions League adventure ended even before it started, with the Greek giants dumped out of the competition by Ludogrets in the third qualifying round.
All of these club struggles have proved highly consequential for the forward's international prospects. He has made only 13 appearances, mostly as a substitute, including at the 2019 Africa Cup of Nations where he came on in the semifinal defeat to Algeria.
But Udeze believes that the Greek reboot could see him play more for the national team: "I believe in Henry, he is a fantastic player. But he is not a regular in the Super Eagles because he is not getting enough playing time in his club.
"If he gets more playing time at his club, for sure he will get his chance in the Super Eagles team."