The total deal for the Argentinian, which has been ongoing for several weeks, is estimated at around 110 billion lire (£36 million) with Almeyda and flying winger Conceicao worth a combined fee of around 75 billion lire (£24.35 million).
Marcelo Salas had also been part of the original deal, but the Chilean striker rejected a move to Parma, preferring to be valued on his own merits and not as a makeweight.
The deal spells an end to suggestions that Christian Vieri is set for a return to Lazio - with the former Real star now likely to remain at Internazionale.
After the fee had been agreed, Crespo expressed his surprise at the move. He said: "I am surprised. I don't know anything and no one has spoken to me,
"My agent is in the United States and (Lazio president Sergio) Cragnotti hasn't shown his face here. I am at a training camp and no-one has called me, so for the moment I am a Parma player.
"I am amazed at this news. I have not signed anything and I have no idea at what stage the negotiations are at."
Having agreed a fee, the two clubs stated that all that remained was for the minor details of the players' contracts to be ironed out.
Conceicao, expressed his bitterness with Lazio's decision to let him be used as part-exchange in the deal. He said: "I am disappointed with what Lazio have done. To be honest I think I deserved a bit more respect after all that I have given to this team.
"I still don't know anything, no one warned me I could be sold and I'll be sorry to leave Rome."
Crespo scored 21 goals last season, only Gabriel Batistuta and Andrei Shevchenko had more. He joined in 1996 from Argentinian club River Plate where he won the league title and Libertadores Cup.
Although the move gives Lazio an amazing amount of talent to call on upfront, with Crespo, Salas, Simone Inzaghi and Fabrizio Ravenelli it has severely weakened their team with no natural replacement for Conceicao and Almeyda's combative style will be greatly missed.
Reports from Italy also state that Lazio will be signing Dutch international Boudewijn Zenden for $15 million (£9.89 million) on Wednesday.
01/03/00 - Lazio Eye Crespo
28/06/00 - Lazio edge closer to Crespo
10/07/00 - Cragnotti: Crespo 99% Certain
