Magic Johnson has upgraded in a big way ... going from a $500k-per-week yacht to a $700k-per-week yacht -- and he's about to complete his 3RD WEEK on the floating mansion.

The NBA legend is currently floating around the Amalfi Coast with Sam Jackson on a boat called the Siren ... which is advertised at $680k-per-week during Summer high season.

It's 73 meters long -- has a movie theater, gym, dining room, hot tub, helicopter pad, an elevator ... and, of course, WiFi.

Johnson and his family boarded the yacht on August 1 after touching down in a private jet.

Some of the family has left -- but Magic and Cookie Johnson are currently traveling with their good friends, The Jacksons.

In previous years, Magic rented out a cheaper yacht -- The Amadeus -- which used to run him about $527k per week.

Seems like he's enjoying the upgrade -- Friday morning, Magic took one of his jet skis out for a ride off the coast of Positano.

Magic just turned 58 on Monday -- HAPPY BIRTHDAY!