Google has made a long-awaited acquisition to bolster its cloud-computing business, a booming industry where it has trailed rivals.

The Alphabet Inc. unit unveiled a deal on Thursday to acquire Looker, a business-intelligence software and big- data analytics platform, for $2.6 billion in cash. The two companies were well acquainted; Alphabet earlier invested in Looker through its venture-capital arm CapitalG.

The...