The 21-year-old has joined the club for an undisclosed fee and will initially join up with the Magpies' Under-23 side.
"At the beginning, I could not believe the opportunity to jump directly from Peru to a Premier League club," Vilca told Newcastle's official club website. "The process had a lot of phases, with all this Covid disaster, so it has been a rollercoaster of emotions.
"I have cried with emotion, not once but several times, because there have been different milestones. At times I have been tense, but now i am very happy and I hope to have a long and successful time in Newcastle.
"It seems a very nice city, the hotel has a very nice view (of the Tyne and Millennium bridges) and I hope to train as soon as possible now. I don't want to lose time - I want to be ready!"
His joy was shared by Chris Hogg, Newcastle's lead player development coach for the Under-23 side, who will coach Vilca during his early days in the north east.
"We're delighted to have Rodrigo here," said Hogg. "He's an exciting attacking player, and we'll be hoping to see that attacking ability.
"We'll be looking to give him the opportunity to improve with us and be a part of Newcastle United's future."
Vilca was handed his senior debut for Deportivo Municipal in 2018 and he went on to score four goals in 24 appearances for the club.
The youngster is Newcastle's sixth signing of the transfer window - but first from outside the UK - following the arrivals of defender Jamal Lewis, winger Ryan Fraser, forward Callum Wilson, midfielder Jeff Hendrick and goalkeeper Mark Gillespie.
Source : 90min