The news was broken by a Colombian radio station which reported the 28- year-old is to return to the Italian club he left to join the Magpies in February 1996 for about the same fee.
Asprilla told RCN, a radio station in Bogota, that his agent, Gustavo Mascardi, had made him aware of Parma's interest, but he said the news that a deal had been struck had taken him by surprise.
"For my career it will be excellent to return to the best football in the world," the striker said. "I feel very good at Newcastle, but the return to Parma makes me happy."
Asprilla added that he was excited by the chance of playing alongside Hernan Crespo, the Argentinian international.
Newcastle initially denied that Asprilla was leaving. Terry McDermott, assistant to the club's manager, Kenny Dalglish, dismissed the report as "rubbish", but he later admitted that a deal had been done.
The Colombian, who combines the unorthodox and the exciting with the frustratingly inept, has been troubled by injuries this season. However, he scored a memorable hat-trick, his only one for Newcastle, when the Magpies beat Barcelona 3-2 in their opening European Champions' League match at St James' Park.
That match stands as a highlight in a season which started badly for Newcastle with Alan Shearer being injured during a pre-season friendly tournament. Newcastle's form has deteriorated over the past two months and they have slid down the Premiership, going eight matches without a victory. They were knocked out of the Coca-Cola Cup by Liverpool, but are still in the FA Cup.
Dalglish has been coming under increasing pressure as the team's fortunes have declined. The Toon Army of supporters have begun to lose patience with a team that, since Dalglish took over, has lost the flamboyance that his predecessor as manager, Kevin Keegan, had introduced.
Recent reports indicated that Dalglish did not have money at his disposal to strengthen his squad, and while the sale of Asprilla will be seen by some fans as another loss of prestige, it will generate funds for transfers.
In addition, Shearer played a full practice match this week and there is the prospect of his returning to the first team by the end of the month, a great relief for all at St James'.
At a news conference at the club yesterday to mark the completion of one year as manager, Dalglish said things at the club were not as bad as some people painted them.
"I was right to take the job and nothing has happened over the last 12 months to tell me I've made the wrong decision," he said. "It is a great club and a great job and I'll never regret coming here. The foundations were there and the support was there when I took over. Everything was in place.
"Until the last eight or nine games, it had looked as though we were heading in the right direction. Those last eight or nine results have not been impressive, but I still think we are on the right lines."
Asprilla will be welcomed by a Parma side who, like Newcastle, need inspiration. Also out of the Champions' League, they were thrashed 5-2 by Sampdoria on Sunday. They are now fourth in Serie A, 10 points behind the leaders, Internazionale.