Terms of the deal weren't immediately available.
The two sides were scheduled to go before an arbitrator in Toronto at 9 a.m., but made a deal on their own ahead of time.
"We were happy to get Teddy signed this morning for the next two seasons," said Lightning GM Steve Yzerman.
Purcell is coming off his first full NHL season. He had 17 goals and 51 points in 81 games for the Lightning while earning $750,000.
In 191 career games with Los Angeles and Tampa, he has 28 goals and 85 points.