Lazaar, 24, joins the club from Italian club Palermo on a five-year contract.
“Achraf is a good, young player with international experience, who has grown his game in Italy,” said manager Rafael Benitez, whose side moved up to fourth in the Championship with a 2-0 win over Brighton.
Murphy, who has won 23 Republic of Ireland caps and featured for his country at Euro 2016.
“When I knew the club was interested, it was a no-brainer for me so I’m happy it’s all done,” he added.
“I think with the squad of players that the club have now, there’s no reason why we shouldn’t be there or thereabouts come the end of the season.”
Ipswich manager Mick McCarthy confirmed Murphy would move to Newcastle prior to the official announcement.
“It’s a really good move for him in his career, at his age, and it’s good for us,” he told BBC Radio Suffolk.
“I told the lads ‘come on, let’s get the elephant out of the room – Murphy’s going to Newcastle, let’s get on it’.”
The striker scored 67 goals in 225 appearances in his five seasons at Portman Road.