Meyer joins Cologne on free transfer after quitting Crystal Palace
"The transfer was only possible because Max was extremely accommodating to us financially," said Cologne director Horst Heldt.
"He can play in several midfield positions, is very confident on the ball and likes to finish chances himself."
Meyer, 25, joined Crystal Palace from Schalke in 2018, but left the Premier League club 10 days ago by mutual consent after struggling to hold down a first team spot.
He is Cologne's second signing in the current transfer window with Nigerian striker Emmanuel Dennis, 23, also joining on loan from Brugge.
With half of the season gone, Cologne are in the relegation places and Meyer could play in Sunday's league game against Arminia Bielefeld, who are one place and two points above them in the table.
Meyer was still a teenager in 2014 when he made the first of his four Germany appearances.
After missing out on a place in the Germany squad which won the 2014 World Cup in Brazil, Meyer captained the German team to the silver medal at the 2016 Olympic Games in Rio de Janeiro.
Meyer says he returned to Germany to help Cologne battle relegation.
"For me, the chance of playing regular football was decisive," said Meyer.
"I want to use the opportunity at FC (Cologne) to present myself at the top level and help the club stay in the league."