The 42-year-old England international goalkeeper made 19 appearances this season, the most recent coming back in January, but he agreed to terminate his contract by mutual consent on Tuesday.
"David has been excellent for us. He's been a model professional and I can't speak highly enough of him," Howe told the club's official website.
"Unfortunately, we've had to make some difficult calls, not just on the goalkeeping front, in terms of picking who we think is our best goalkeeper, but financially we are having to readjust.
"The club has to be streamlined and it has to make sure its manageable, so we are in the process of doing that.
"We will have to make some difficult decisions, but it will all be for the benefit of the club. This is part of that, but we thank him for everything he has done for the club and we wish him well in the future."
James, who earned 53 caps for his country, is now looking for the ninth club of his 25-year playing career.