In an interview broadcast on ABC Radio, Conroy said he hoped to announce the commencement of an agreement with the Tasmanian Government "in the next few days".
"Tasmania unfortunately [has] had the slowest and most expensive broadband in the country," he said.
iTnews previously reported that the FTTH rollout in Tasmania could begin as early as June or July.
At the time, Conroy confirmed that some 250,000 Tasmanian homes and businesses would be connected via the FTTH rollout.
Remaining residents would be served by higher-speed wireless services, he said.
Tasmanian residents are also starting to benefit from the imminent launch of the Basslink cable with a broader range of ADSL2+ services now being offered.
Netspace this week announced it had rolled out DSLAMs into three exchanges in Hobart and Launceston and has another nine exchanges in various stages of build.
Internode also brought its ADSL2+ services to Tasmania back online late last year.