Odom has played over 1,000 games over a 14-year career in the NBA, but has been a free agent since the end of last season after being released by the Los Angeles Clippers.
Baskonia, currently ninth in the 18-team Spanish Liga Endesa, have the option to extend the deal until the end of the season.
Odom played a key role on the Los Angeles Lakers side that won back-to-back NBA titles in 2009 and 2010, but has struggled to hold down a roster spot since leaving the Lakers the following year.
The 34-year-old power forward has also endured a troubled time off the court as he was sentenced in December to three years probation and three months of treatment for alcohol abuse for driving under the influence and split from reality TV star wife Khloe Kardashian.
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