Biaggi, a multiple grand prix world champion, announced his retirement from the sport earlier this week.
His career spanned three decades and included four straight 250cc world titles and two World Superbike crowns.
Across that time the 'Roman Emperor' and Rossi often went head-to-head, their on-track rivalry fuelled by off-track antipathy.
Despite such strained relations, Rossi said it would be the fierce battles and long rivalry that he would remember.
"For me with Biaggi it was like a special relationship, because we were great, great rivals for a long period," Rossi explained.
"Fighting for the championship in 500cc and then MotoGP was very exciting.
"I think the year we were closest was probably 2001 because it was the last season with the 500 two-strokes and everybody wanted to win, so the battle was very hard on the track and also off it.
"Out of the track our relationship was not fantastic, but anyway he was a great rival [of whom] I have great memories."
Rossi has faced questions about his own future in the sport following two winless seasons with Ducati, and found himself the subject of intense speculation in the aftermath of Marco Simoncelli's death at Sepang in 2011.
He said however that every rider knew when the time to quit was, and that Biaggi's decision ensured he left the sport on a high.
Biaggi clinched his second WSBK crown by just half a point this year.
"I think it is useless to speak about this [Biaggi's decision to retire] from the other riders," Rossi said.
"Everyone knows the right moment to stop.
"Biaggi will stop at the top of WSBK. At 41 he is quite old, so it is a life decision.
"But anyway [there] remain good memories and great battles together."
- Sports & Recreation