Siegel will replace Patrick Crawford, who is retiring after six years in charge of the ethical bank, which lends solely for social purposes.
Siegel, who will take charge at the end of July, has more than 30 years of corporate banking, social investment and business consulting experience, according to a Charity Bank statement.
He has been managing director of Big Issue Invest, the social investment arm of the Big Issue Group, since 2008.
During Siegel’s time at the helm Big Issue Invest has grown from offering a book of social enterprise loans worth about £2m to offering a wide range of social funds under management worth more than £65m.
Siegel said in a statement: "Charity Bank has a well-earned reputation and one of the strongest brands in our sector.
"Its mission to use money for good was a key factor in my decision to pursue this opportunity."
George Blunden, chair of Charity Bank, said in a statement that Siegel would bring experience and a "deep understanding of the social sector" to the role.
Blunden said Charity Bank, which was founded in 2002, was moving towards "sustained profit", adding: "Ed is the right person to lead it as we enter this new phase and take action to address how we can best meet the future expectations and needs of the social sector."
Last month, Charity Bank announced it had lent more than £15.2m to the social sector in the first three months of 2018 – more than during any previous quarter in its history.
Blunden said Crawford had "led Charity Bank with great aptitude and passion".
He added: "He leaves behind a bank that is achieving record loan and deposit growth and social impacts, for which he should take great credit."
Asked how much Spiegel would earn, a Charity Bank spokesman said: "The bank has historically operated with a maximum ratio of nine to one between the highest and lowest-paid members of staff, and this continues to be the case."