Porto said they will receive 45 million euros - or £38m - for Colombian Rodriguez, and 25 million (£22m) for Portuguese international Moutinho, both on five-year contracts.
The sums involved are quite incredible: Rodriguez becomes the most expensive player in French football history, ahead of Paris Saint-Germain's Zlatan Ibrahimovic and Thiago Silva. For a player who has yet to prove himself on a major stage, the fee is unprecedented.
And this could just be the start. According to Eurosport reporters in Paris, the club are far from done with their summer purchasing and are set to announce a huge deal for Atletico Madrid striker Falcao on Monday.
Manchester United defender Patrice Evra and Barcelona goalkeeper Victor Valdes are also thought to be close to agreeing transfers to the principality.
What makes the story all the more incredible is that all this money is being spent by a newly-promoted team: Monaco have only just returned to Ligue 1 after being taken over by Russian billionaire Dmitry Rybolovlev in 2011.
Despite the fact that they have been in the second tier for two years their emergence poses a threat to the domestic dominance of Paris Saint-Germain, who won their first Ligue 1 title in 19 years thanks to Qatari investment.
And as for Friday's signings? Moutinho and Rodriguez, 26 and 21 respectively, were instrumental in helping Porto clinch a third consecutive league title this season.
Moutinho is a consistent hardworking midfielder noted for his tactical awareness while Rodriguez has great dribbling skills and the ability to deliver dangerous crosses.
Monaco are at odds with French football authorities over tax exemptions but they have attracted many leading players helped by the fact that, under the principality's laws, foreigners do not pay tax on their wages.
The French League has ruled that the club must move their head office to France by the start of June next year, meaning players would pay tax in France.
THE FRENCH VIEW - MAXIME DUPUIS, DEPUTY EDITOR, EUROSPORT.FR
The size of the fee is crazy but not really a surprise considering that Monaco's owner Dmitry Rybolovlev is a kind of Roman Abramovich figure. Even if it's a huge price it's not a problem for Monaco because of the money they have.
Furthermore you have to remember that Monaco have just been promoted from Ligue 2, so you have to pay a lot to convince players to join. There is a logic to it.
I think it's an intelligent move because we all know that Porto has great players - remember what Jose Mourinho did, bringing Porto players like Carvalho and Ferreira to Chelsea. These two guys are very good.
For the moment, I don't think they will be an immediate danger to PSG - but that answer might change on Monday when they are expected to sign Radamel Falcao from Atletico Madrid. And they won't stop there - if they continue with these kinds of recruitments, they will definitely be a threat.