Dembele, 24, joins an Atletico side that is leading La Liga with three games in hand, the club are also set to take on Chelsea in the round of 16 in the Champions League next month.
Atletico needed to bolster their attacking line after the departure of veteran forward Diego Costa last month.
The France international found the back of the net once in 16 league appearances for Lyon this season and despite being tied to the club until June 2023, the club revealed he was "looking for a change".
Dembele will not be immediately available to Atletico coach Diego Simeone as he is still recovering from a broken arm suffered last month.
Lyon also announced that Slimani, 32, joins on loan. The Algeria international joined Leicester in 2016 on a then-club record £28 million deal, but had loan stints at Newcastle United, Fenerbahce, and AS Monaco. He won the Africa Cup of Nations in 2019 with Les Verts.