Blignaut, 25, is the second of 15 white rebel Zimbabwean players stood down by the Zimbabwe Cricket Union (ZCU) to head to Australia following all-rounder Sean Ervine's move to Western Australia.
TCA chief executive David Johnston said Blignaut would go some way towards replacing international Shane Watson, who is awaiting clearance to return to Queensland.
Johnston said Blignaut would arrive here in late August.
"He can bowl very fast, I think that's something we are looking for, and obviously he's very handy down the order as a batsman," Johnston said.
"So I think he goes part of the way to replacing Shane Watson, who batted a bit higher in the order."
Blignaut said in a statement from Harare that he was looking forward to playing for Tasmania and "determined to give it my all".
He has played 15 Tests, scoring 638 runs at an average of 24.53 and capturing 51 wickets at 32.62.
He has also played in 47 One-day Internationals, scoring 533 runs at 19.03 and taking 41 wickets at 43.39.
Johnston said there were negotiations with unwanted One-day International batsman Michael Bevan, who is considering whether to accept an offer from New South Wales or sign with Tasmania.
"We have been talking for two or three weeks now, so we are getting fairly close to the end of it," Johnston said.
"We are hopeful to hear something from Michael's management company in the next few days."