Alesi, 37, has been signed to drive the remaining five races of the season for Jordan alongside his new teammate Italian Jarno Trulli, starting at the Hungarian Grand Prix on August 19.
Despite being new to the F1 team, the former Tyrrell, Ferrari, Benetton and Sauber driver said his relationship with Irishman Jordan went back many years.
"It was with Jordan that I won the 1989 Formula 3000 title. In those days, I was just leaving Avignon and Eddie simply suggested that I live with him," he expalined. "I accepted, and lived with him and his family for a while. When I had the opportunity to enter Formula 1 with Tyrrell ... it was Eddie who organised the contract for me.
"We promised then that if he ever got his own team going in F1, we'd resurrect our partnership. For various reasons over the past few years, that hasn't been possible. But, at last, we're back together."
Jordan was also keen to stress that, despite constant rumours about the move, he had not negotiated a deal with Alesi until the Frenchman had decided to leave Prost.
""We are old friends, so this is normal. But we only struck this deal once Jean was free to join Jordan," Jordan said when announcing the switch on Wednesday.
""Alain Prost and I are also very good friends and it is important to make clear that there is absolutely no animosity over the course of events which have lead to Jean joining Jordan," he added.