Laverty, 32, rode for the team during this year's campaign, claiming a best result of 13th at Jerez.
Parkes meanwhile will make his MotoGP debut, having spent the majority of his career competing in World Superbikes or Supersport, in which he has twice finished runner-up.
The 31-year-old Australian, who raced for PBM in WSBK in 2009, replaces Yonny Hernandez, who signed a full-time deal with Ducati's satellite Pramac squad last month.
"We learned so much in year one that I'm delighted [team owner] Paul [Bird] has given me the opportunity to continue with the project," Laverty said.
"Everyone has told me that year two is much easier so the aim is to put into place what we have learned and to raise our game accordingly.
"The class is going to be a lot tougher with the new production bikes but our aim is to consistently score points."
Parkes said moving into MotoGP would be the realisation of a dream, adding: "Firstly, I'd like to say a massive thanks to Paul Bird for the opportunity to work with his team once again; I'm really looking forward to it.
"This is the premier class and it's every rider's dream to race in MotoGP.
"I know this is going to be a tough season but I'm certainly up for the challenge, I can't wait to get started."
Bird said his new pairing would help the team deliver on the groundwork it has put in place over its first two seasons in the category.