The 35-year-old left Madrid on the expiration of his contract, having helped Los Blancos to five LaLiga titles and four Champions League triumphs during his 16-year spell in the Spanish capital.
Ramos, who wanted a two-year commitment from Madrid, claimed in June that he had belatedly accepted a one-year contract offer from the club, only for it to be withdrawn.
He has now joined PSG, linking up with mooted Madrid target Kylian Mbappe and former Clasico rival Neymar in Paris, with the centre-back signing a two-year deal.
Ramos not only brings defensive nous and experience – he helped Madrid to 206 clean sheets – but he is the only defender to score 100 goals while playing in one of Europe's top five European leagues since the turn of the century.
Earlier in the week PSG signed Moroccan defender Achraf Hakimi on a five year deal.