The two have often clashed as rival race organisers but their frustration at the way the UCI is running the sport has helped rebuild their relationship and brought them closer together.
"We both represent the history of cycling, each in our own way," Vegni told La Gazzetta dello Sport.
European Cycling Union president David Lappartient also attended the Grande Partenza of the Giro d'Italia in Sardinia with Italian Federation president Renato Di Rocco, as the political manoeuvring and election campaigning gets into gear.
Lappartient has yet to confirm he will run for the role of UCI president and so challenge the incumbent president Brian Cookson but many traditional European federations and race organisers seem ready to back a change of leadership at the UCI elections in September.
"I really wanted to be at this year's race, it's special and you can feel it. Mauro and his team have done a great job and I can't wait for the spectacular stages to happen," Prudhomme told La Gazzetta dello Sport.
"The Tour, the Giro and the Vuelta are working in the same direction. We get on because we share the same passion, the same ‘Amore Infinito' as they at the Giro.
"There's a special feeling at the Giro this year, one of great cycling as when the likes of Fausto Coppi, Bartali and Merckx were racing. Whoever wants to follow them in the history of the sport has to win the Giro d'Italia. Whoever wins this 100th edition will have a special place in the history of our sport."
This year the L'Equipe sports channel on terrestrial French television has the right to broadcast the race. L'Equipe is owned by ASO, just like the Tour de France.
"I've been watching the Giro every day from Paris. There's a lot of interest in France for the 100th edition of the Giro d'Italia this year because it's transmitted live on L'Equipe TV. Everyone is naturally cheering for Pinot," Prudhomme said, while also showing admiration for race leader Bob Jungels and Fernando Gaviria of Quick-Step Floors.
"Bob is talented, he's young and talks lots of languages. He's always kind, smiles and is good on television. Fernando Gaviria is the same. I saw him win Paris-Tours last year. Immediately after he won the stage in Cagliari, I got a message from the president of Colombia and Nobel Peace winner Juan Manuel Santos. He was really happy," Prudhomme concluded.