It has also announced plans to retrain 800 members of staff already working at the location so they can take up roles with the supplier.
The chief executive of SSE, Ian Marchant, said he was "very pleased" to reach an agreement over the customer service site.
He added: "The acquisition of the site provides us with the capacity to expand our customer service operations and recruit many new skilled people at a time when our business has achieved significant growth and is continuing to expand."
The energy provider's plans to expand its customer service operations have been revealed after it also announced new carbon emission reduction targets.
SSE has stated it plans to half the amount of emissions it produces in electricity generation by 2020.
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