Remedy software is widely used in the UK, in companies such as BT, the RAC and Abbey National. The Remedy User Group gave a cautious welcome to the move. It said it provides some relief after a period of uncertainty.
Peregrine's future became uncertain earlier this year when it came under investigation by the US Securities and Exchange Commission after allegations of fraud were made by auditors.
Remedy User Group steering committee member Saleem Haq said, "It is a good result for Remedy to be bought by a reputable software house. The immediate future for Remedy users is good and it ends a period of uncertainty.
"We will, however, be looking at what emerges as the sale goes through and will want to ensure that existing levels of support continue. We hope BMC recognises that Remedy is a trusted product."
The $350m (£224m) sale of Remedy follows a long period of financial uncertainty at Peregrine. However, earlier this year Remedy's buyer BMC itself posted second quarter results which showed a 10% drop in revenues and a loss of $34.5m on net income of $5.2m
In June, Peregrine laid off nearly half of its staff - about 2,900 people. This came after Arthur Andersen and then KPMG were successively hired and fired as auditors as accounting concerns emerged.
In a statement this week, Peregrine's chief executive Gary Greenfield said he expected the company to emerge from Chapter 11 protection upon the resolution of financial and legal issues.