Radwan joins a Leicester team that sit fourth in the Premiership and are through to the last 16 of the Champions Cup after finishing third in their group.
He said he had “nothing but positive memories” of his time at Newcastle.
“The supporters and everybody at Kingston Park have always been great with me, and I can’t express how much that has meant,” he added.
Falcons consultant director of rugby Steve Diamond said he understood that some fans would be disappointed by Radwan’s departure.
“Adam is an ambitious player who came to us and expressed his desire to take up this opportunity with Leicester,” said the former Saracens, Sale and Worcester boss.
“There’s absolutely no animosity between Adam and ourselves, and he will always be welcomed back here as a player who has given tremendous service to this club.”
Leicester are next in action with an away game against Gloucester on Saturday.
