The deal, which is worth $386 million, is expected to be completed in the fourth quarter of the year.
A cash payment of $329 million will be made by Bank of New York Mellon, with the remainder being paid in the form of an equity consideration.
Included in the sale will be Insight's external fund management operation, which oversees assets worth around Â£80 billion for a number of pension schemes, intermediaries and third party distributors.
"We believe Insight is better able to focus on developing its specialist external franchise outside the group," wealth and international director of Lloyds Banking Group Jo Dawson stated.
Earlier this month, the bank - which is 43 per cent owned by the taxpayer - announced a first-half loss of $6.76 billion, down from a profit of $4.73 billion in 2008.