Vodafone is carrying out the acquisition to strengthen its enterprise business in the UK and abroad by expanding its network and creating cost-saving opportunities.
CWW provides high-speed telecoms services to companies including Tesco and the police.
It marks an attractive proposition for Vodafone, as the telecoms company moves to grow its corporate business at a time of weak consumer growth.
CWW's fibre cable network is expected to relieve pressure on Vodafone's mobile network, while the latter's enterprise business will gain a boost because CWW already has contracts providing voice, data and hosting services to government departments and companies, including Tesco.
Cable & Wireless directors will unanimously recommend that shareholders vote in favour of the takeover.
Vitorrio Colao, chief executive of Vodafone group, said: "The acquisition of Cable & Wireless Worldwide creates a leading integrated player in the enterprise segment of the UK communications market and brings attractive cost savings to our UK and international operations."
Vodafone has beaten off a rival approach from Tata Communications, the India-based telecoms company.
Follow Matthew Chapman at @mattchapmanUK