Hendrick who has 54 caps for his country, left the Clarets in June and was a free agent.
He was signed by Burnley manager Sean Dyche for a record fee of £10.5m in 2016 but was unable to agree on a new contract.
Jeff Hendrick is Newcastle’s first signing since the collapse of the proposed takeover in July.
Steve Bruce has said previously that he hopes to bring in a couple of signings before the transfer window closes.
“It’s a massive club and playing over the years, going to the stadium, it’s one of the best stadiums to play in, so I just want to get playing there,” said Hendrick.
“I’ve had over 100 games in the Premier League but I want to keep going and keep improving with a different team. It’s going to be different for me, the demands with the bigger stadium, the crowd, how big the club is, so I’ve got to take that on and keep pushing myself and striving to get better.”
Bruce added: “I watched him when he was at Derby, then he went to Burnley for a lot of money and couldn’t afford him, so I missed out then!
“He’s an experienced international football who can play all across the midfield so we welcome him aboard. He’ll be a big asset to us, on and off the pitch.”