Parker will now turn his attention to masterminding a swift return to the Premier League, while Newcastle manager Benitez will continue his discussions with owner Mike Ashley - who was watching on in west London - over a new contract.
The Spaniard, however, hinted that his willingness to extend his three-season reign will hinge on Ashley's vision for Newcastle.
He was capped 18 times by England and played almost 600 professional games, mainly in the Premier League for Charlton, Chelsea, Newcastle, West Ham and Tottenham, before ending his career at Fulham in June 2017.
'He was talking with me and the team.
He lost his first five games in charge as Fulham were relegated from the Premier League, but then won three of the next four matches.
"I can see the potential of this massive club and hopefully we can do things in the way that would be good for everyone".
He said he was delighted to take the job full-time and added: "I thank the chairman for entrusting me with this responsibility, as well as the support and encouragement that both he and [vice-chairman] Tony Khan have provided me. He didn't say anything special, but was congratulating the team".
"I'm really happy to play for Newcastle United, to be here with my teammates, with the club, so we will see what happens", he told the club's official website, endearingly not playing it cool at all with regards to his future.
Goals from Jonjo Shelvey, Ayoze Perez, Fabian Schar and Salomon Rondon sealed a comprehensive win at Craven Cottage, with Newcastle leapfrogging Bournemouth on the final day to finish 13th in the Premier League.
'I've been trying to do my best to give them something back.
"Scott was courageous to accept a very hard challenge in February when appointed as our caretaker manager", Khan said.
"We will have a meeting hopefully next week and we will see where we are", Benitez said. And we were vulnerable on the break.
Activists Have Scaled The Sydney Harbour Bridge
About 5.15am (Tuesday 14 May 2019), security staff operating on the Sydney Harbour Bridge observed several people on the bridge. The environmental activist group has been providing live coverage of the protest, releasing footage and images .