The Electronic Secretary (1949) was the first telephone answering machines available in America (even earlier systems were used in Europe, but strangely forbidden in America due to resistance from AT&T and the FCC.)
They were used exclusively for businesses at this time. The original model recorded on wire and used a pre-recorded, professionally voiced 45 rpm record as the outgoing message. Succumbing to consumer demand, the Bell System companies and GTE rented this machine to mostly higher income residential customers by the early 1960s (the rental fees were big.)
In spite of it's availability (and the machines used cassette tape by the '70s), The answering machine was still fairly rare however and never really took off in America until the breakup and deregulation of AT&T in 1983 when they were finally sold direct to consumers outside of the phone companies.