Colao, who has been chief executive since July 2008, will be replaced by chief financial officer Nick Read.
Vodafone appointed Nick Read as group CFO in April 2014.
He joined Vodafone in 2001 as Vodafone UK Finance Director before being appointed Vodafone UK Chief Commercial Officer then Vodafone UK Chief Executive.
"Nick has been the co-architect of the Group's strategy together with Vittorio, combining extensive worldwide operational and commercial leadership with world-class financial acumen", commented Gerard Kleisterlee, the Group's Chairman.
Mr Kleisterlee added: "Nick has been the co-architect of the group's strategy together with Vittorio, combining extensive worldwide operational and commercial leadership with world-class financial acumen". I am confident Vodafone will benefit greatly from his experience, insight and wisdom in his new role as Group Chief Executive.
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Vodafone delivered an attributable profit of €2.5bn, compared to a loss of €6.3bn in 2017 when the company incurred a one-off €4.5bn charge in relation to merging its India business with the country's mobile phone provider Idea Cellular Limited.
For Read it's a "step-up" role, after a good track record at Vodafone, said James Ratzer, a telecoms analyst at New Street Research in London.
This has led to a mixed full year to 31 March 2018 operating performance, although one that looks pretty decent overall.
'The UK remained the sick man of Europe during 2017/18, with service revenues down 3.6% organically to €6.1bn, versus growth of between 1% and 2.6% in the other main markets, ' says Megabuyte analyst Philip Carse today.
Excluding the negative impact of net roaming declines in Europe, the benefits of settlements in the United Kingdom and Germany and the introduction of handset financing in the United Kingdom, organic adjusted EBITDA grew by 7.9%.
Vodafone's results showed underlying earnings - the company's preferred profit measure - rose 12 per cent on an organic basis to €14.7 billion, ahead of the company's guidance of 10 per cent organic growth. The deal to acquire Liberty Global's German and Eastern European businesses allows Colao to leave having mostly solved years of on-and-off talks with billionaire John Malone's cable company about a potential tie-up to better compete with incumbents like Deutsche Telekom. "Our primary focus continues to be to accelerate the "Digital Vodafone" programme, which we believe is a unique opportunity to enhance our customers' experience, generate incremental value and improve cost efficiency".