Charles Jarrold, managing director of Southernprint, said he was disappointed with their departure, but said it reflected the "unique position that BGP finds itself in".
He said: "We are looking to fill both positions, although whether this will be through internal promotion or external recruitment, it’s too early to say.
"However, I am pleased that Southernprint’s excellent reputation for quality and service is already leading to considerable interest in these roles."
Both staff members are understood to be on gardening leave for the next few months, before joining BGP.
David Holland, chairman of BGP Group, said the moves had been finalised for when the pair reach the end of their notice period.
Two sales managers quit Southernprint for BGP roles
Southernprint sales managers Adrian Clark and Peter Helfrich have resigned to join web offset printer BGP.