A spokeswoman said on Tuesday the current contracts and salaries of the affected staff would be honoured for the next 12 months, and the positions would be kept in Zurich.
Staff who are not prepared to sign new contracts with HCL will leave the company, she added. The plan was first reported by Swiss newspaper TagesAnzeiger.
"Credit Suisse has been working with external providers worldwide for many years, as is common in the industry," the spokeswoman said. "HCL has an excellent reputation in the market and was selected as a partner following careful evaluation."
Credit Suisse, which employs 17,020 people in Switzerland, is currently around two thirds the way through its plan to cut Swiss headcount by 1,600 by the end of 2018, the bank said.
The lender has had to adapt to a squeeze in banks' profitability due to the mix of negative interest rates, political uncertainty and sluggish economic growth.
It is also planning to cut roughly 1,500 jobs in London by the end of next year, according to a person familiar with the matter, part of efforts to cut costs globally.
Last year, Zurich-based Credit Suisse pledged to cut another 1 billion Swiss francs ($1 billion) in costs as the bank responded to challenging markets which have made it tougher for banks to make money.
The bank is aiming to reduce its global headcount of 46,640 staff by 5,500 by the end of 2017.