The 24-year-old World Cup defender has spent the last three years with Ironi Ashdod in Israel's Premier League.
"I am happy because I have made a big step in my career by joining Hearts," Oshaniwa told BBC Sport.
"Starting from Nigeria and playing in Israel to land here in Scotland is a big progress for my career."
Oshaniwa, who has 17 caps, played in all of the Super Eagles' matches at the 2014 World Cup in Brazil.
But he only made 13 appearances last season as Ashdod suffered relegation from Israel's top flight.
"I thank God for the opportunity," said Oshaniwa of his move to Edinburgh. "I also thank Hearts too for the confidence and determination to bring me here.
"My immediate focus is to give my best and hopefully achieve many success stories with the club."
Oshaniwa only joined his new team-mates in training for the first time on Saturday morning and Hearts are still awaiting international clearance.
So it is too soon for the left-back to feature as Robbie Neilson's side kick-off their top-flight season against St Johnstone at Tynecastle on Sunday.
The head coach was delighted that the player who began his career with Kwara United before moves to fellow Nigerian clubs Lobi Stars and Sharks had finally arrived in Scotland.
Hearts, who were promoted after winning the Scottish Championship title, have already started their season with a 4-2 victory over Arbroath in the first round of the Scottish League Cup on Thursday.
"It's been a long process to get him here in Edinburgh, but he's here now and he's desperate to get started," added Neilson.
"He's a top-quality player and he'll bring a lot of qualities to our squad. We're all very happy with this move."
Nigeria left-back Juwon Oshaniwa has signed for Hearts on a three-year contract saying he is advancing his career by moving to Scottish football.