The duo, who came through the Forest youth ranks and arrive for an undisclosed fee, have signed "long-term deals" at St James' Park and will return to the City Ground on loan for the 2014-15 Championship season.
The transfers have been the cause of some unrest at Forest, with manager Stuart Pearce thought to be furious about the departure of Lascelles and Darlow, but the former said a move to Newcastle was impossible to turn down.
"As soon as I found out about the move I was over the moon," he said. "It's a huge step up for me. Newcastle are a club with a massive fanbase, a big history and an unbelievable stadium.
"First, I am going back to Forest for another season and that will be great for my development. Hopefully I can come here next summer an even better player."
Darlow echoed those comments, adding: "I'm delighted for it all to be sorted and I can't wait to get started here at Newcastle. The loan back is going to be another year but it gives me time to develop my game further before I return.
"I'm looking forward to the future."
And Newcastle manager Alan Pardew is delighted to add the two hot prospects to his squad.
"It is a real coup to have signed two of the finest young talents in English football outside of the Premier League," he added. "Jamaal and Karl will be a big part of the future of this club.
"They have both performed outstandingly in the Championship over the last couple of years and I have no doubt they will be able step up to this level once they return from their loan at Nottingham Forest."
Lascelles and Darlow were both first-team regulars for Forest last season and are aged 20 and 23 respectively.
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