One of Europe’s most prominent former bankers is joining a bitcoin startup.

Antony Jenkins, the ex-chief executive of Barclays PLC, said he has joined the board of directors of Blockchain, a London-based startup that provides services related to bitcoin and cryptocurrencies. The company, named after the basic technology that creates the shared network used to move and track bitcoin, raised $30 million in an initial fundraising in 2014.

The...