The 26-year-old has not featured much in pre season, having recovered from blisters after an early game and missing the USA tour to stay home and complete a move elsewhere.
Muto, 26, has played 25 times for Japan and featured in one game at the recent World Cup, the 1-0 loss to Poland.
The transfer fee is believed to be around 11 million euros (£9.8 million, US$12.8 million).
"The clubs were talking for a long time and now I'm focused on the season to help my team mates to get the points to do well this season", said Rondon.
Muto is Newcastle's fifth signing of the transfer window following the arrivals of Martin Dubravka, Ki Sung-yueng and Fabian Schaer on permanent deals and the loan capture of Kenedy.
A day earlier, Benitez expressed displeasure with his club's summer activity when was not pleased with the Magpies' performance in a thrashing at Portuguese club Braga.
Having already been a target of Benitez's previously, the report says Ings is now "back on the agenda" and "interested in heading to Tyneside".
"So if you're taking that stand, you have to be very conscious of what you are doing, and what you are trying to do is publicly force the owner into spending more money". Put it all together and you understand why the fans need to be concerned.
"He, together with Yoshinori Muto, will give us different options, and will improve the competition between the strikers, which is always positive for the team".
A tempestuous pre-season at St James' Park has worsened with the squad refusing to undertake contractual TV obligations as they make a stand over incentivised payments from their club.