Nuance Communications Inc., a Burlington company known for its Dragon brand of speech-recognition products, said Tuesday that it has agreed to buy Ditech Networks Inc., which offers such voice technology services as PhoneTag voicemail-to-text services.

In a press release, Nuance said it has agreed to acquire Ditech Networks for $1.45 per share in cash, representing a total enterprise value of about $22.5 million, net of Ditech Networks’ cash as of the signing date.

Among other things, Nuance said that Ditech Networks’ PhoneTag service will enhance Nuance’s Dragon voice-to-text services business.

The transaction has been unanimously approved by the boards of directors of each company, Nuance said. The transaction is expected to close late in 2012, subject to Ditech Networks stockholder approval and other closing conditions.

Ditech Networks is headquartered in San Jose, Calif.