The move is part of plans announced three months ago by new management to revive Rexam's flagging fortunes.
In a statement Rexam, formerly Bowater, said it was "inappropriate" at this stage to speculate about how much the sales might raise.
However, the businesses earmarked for disposal have a combined annual turnover of pounds 303m, operating assets of pounds 161m and made an operating loss of pounds 2m.
They cover some packaging and coated paper businesses, printing, beauty, food and beverage and some industrial operations. Only healthcare and building and engineering are unaffected.
"The decision to sell these companies reflects Rexam's increasing focus and the strengthening of its interests in its seven sectors," said Rolf Borjesson, the Swedish chief executive who succeeded David Lyon in July.
"We are seeking to improve the returns from our businesses and will concentrate on those areas that offer the best growth opportunities."
Rexam, which has already sold businesses with combined sales of pounds 216m this year, has appointed a full-time management team called Octagon to carry out the disposal programme. It will be led by David Jones, who has been chief executive of Rexam's containers division since 1995.
"The object is to achieve an orderly and efficient sale with the least disruption to employees, customers and suppliers," said Mr Borjesson. "They are all sound businesses and we hope to get a decent price for them."
Mr Borjesson expects Rexam's staff numbers to fall to about 23,000 once the disposal programme is complete and to see its wage bill fall accordingly.
Rexam's objective is to achieve a 25 per cent return on net assets across the group, but Mr Borjesson stressed that the decision to sell off non- core assets was not solely based on this criteria.
Shares in Rexam, as high as 409p three months ago, rose 4.5p to 341p, largely on relief that the company was taking action on promises made at the interim results stage.
Rexam has been trying to win back favour with investors in the City ever since it issued two profits warnings in three months last year after being hit by volatile raw material costs and customer destocking.
In July Rexam was ejected from the FTSE 100 index of blue chip companies after the shares hit a four-year low.
In the six months to June Rexam reported pre-tax profits of pounds 77m, down from pounds 112m a year ago, and warned that it was cautious about the outlook for the second half of the year, blaming generally flat industrial demand, particularly in the UK and continental Europe.