Bayern made the announcement on Tuesday, a day prior to his 26th birthday:
In an accompanying statement on their official website, Bayern chief Karl-Heinz Rummenigge said:
"We're delighted we've been able to complete this transfer. Signing James Rodriguez was our coach Carlo Ancelotti's biggest wish, following their successful spell working together in Madrid. James is a very versatile player. He's a goalscorer himself, he sets up a lot of goals and on top of that he's great from set pieces."
Marca's Chris Winterburn supplied further details of the loan deal, which appears to be something of a bargain for Munich, while ESPN FC's Liam Twomey hailed the strength in depth he will bring:
The playmaker joined Los Blancos in the summer of 2014 after a starring display with Colombia in the World Cup:
He immediately made an impact, putting together an excellent first campaign in the Spanish capital.
Rodriguez suffered an injury while on international duty early in the 2015-16 season, however, and never got back on track. By the time Zinedine Zidane replaced Rafa Benitez as manager, he had tumbled down the pecking order, and the new boss never fully trusted the Colombian.
Transfer rumours intensified toward the end of that season, and things didn't change in the 2016-17 campaign. The emergence of young starlet Marco Asensio and improved form of both Isco and Lucas Vazquez only limited his chances further, and Rodriguez didn't even make the bench for Real's UEFA Champions League final match against Juventus.
While his recent campaigns may have been disappointing, Rodriguez remains a special talent capable of incredible things with a ball and he still contributed much during his time in Spain.
Per Squawka Football, he produced 28 goals and 27 assists in La Liga over the last three seasons, more than any other midfielder, a feat made all the more impressive considering he's not been a regular starter.
With Real no longer under a transfer ban and Rodriguez struggling to get the game time he would enjoy elsewhere, the timing of the deal makes sense and Zidane is free to invest in a replacement.
At the Allianz Arena, Rodriguez's versatility should serve him well. Ancelotti could use the former AS Monaco man in his preferred role behind the striker, but he's also comfortable in a central-midfield position or on either wing.
Arjen Robben and Franck Ribery are now 33 and 34, respectively, and so Rodriguez could help replace the pair.
In a more central role, Rodriguez's tremendous ability as a creator would make him a fine fit for the 4-2-3-1 formation, a system Ancelotti used on plenty of occasions last season.