The move is part of the East Anglia-based firm's wider strategy to transform itself into a national firm and boost turnover from £56.4m to £110m in the next five years.
Mills & Reeve private client head Matthew Hansell said: "We want private client turnover to get to approximately £25m. We reported £11.7m for the last financial year, which is roughly 20 per cent of overall turnover. This group is profitable for the firm so it's worth investing in.
"To have a successful national firm we have to have a full-service private client team."
Addleshaws is dispensing with its family practice to focus on a standalone trust practice, which was once combined with the family group.
A source close to the firm said: "The family group doesn't fit in with the firm anymore. Addleshaws wants to focus on finance and corporate. While the trusts element of private client works well with this, family doesn't."
Mills & Reeve's new offices will open in February 2008 with the three-partner and eight-associate team, headed by David Salter, becoming part of its drive to expand in private client.
Salter's team includes partners Nigel Shepherd and Philip Way.