The Poland defender agreed a deal with the Championship winners, subject to international clearance.
Centre-half Augustyn, 27, made 18 appearances for Gornik Zabrze in his homeland last season and moves to Edinburgh after enjoying a nomadic career.
The Pole started his career in England at Bolton before spells with Legia Warsaw, Rimini, Catania and Vicenza.
Neilson had been in the market for a stopper since skipper Danny Wilson left the Jambos in the summer after triggering an early release clause.
Augustyn won three Poland U21 caps between 2009 and 2010.
Blazej told Hearts TV: “I’m happy to be here. It’s a great opportunity for me to play here, in front of thousands of people.
“Everyone is so kind and I’m happy. The only thing is that I haven’t spoken English for a long time so that’s the one thing that I have to improve…quickly!
“I think I’m good in the air and I’m aggressive. I will try to show all these things on the pitch. The more experience you’ve got is better for the player. I will try to show my best on the pitch. I will do my best for Hearts.
“The first things are that I want to get fit, be strong and show all my good things on the pitch. With Hearts, I hope we go to the top six and we do as much as we can.”