It will be a conditional clearance. Western Digital is making fairly sizeable divestitures, said one person, declining to provide details because of the sensitivity of the issue.
The European Commission is likely to approve the deal next week, ahead of its scheduled November 30 deadline for a decision, the people said.
Western Digital shares were up 5.8 percent to $26.46 by 1708 GMT.
The EU competition watchdog opened an in-depth investigation into the deal in May. It also investigated a plan by Seagate Technology to buy Samsung Electronics' hard disk drive, citing concerns that the deals would shrink the number of players in the sector.
It approved the Seagate and Samsung deal last month without any conditions.
Western Digital, the world's No. 2 player in the hard drive sector, and No. 3 player Hitachi in March unveiled the proposed $4.3 billion deal, which will give Western Digital an edge in developing next-generation storage technology.
Flash drives, or solid-state drives, use less power, are faster and are widely viewed within the industry as the future of the disk drive industry. They are increasingly being built into laptop PCs and tablet computers.
(Reporting by Foo Yun Chee, editing by Juliane von Reppert-Bismarck and Elaine Hardcastle)