Following talks, the deal has been completed for around $1.75 billion, including just $250 million in cash.
Lehman's highly-regarded broker-dealer wing incorporated its equity, fixed income and mergers and acquisitions advisory businesses.
It is hoped that the takeover, and the forthcoming merger between the brokerages, will encourage Lehman customers to stay with the firm.
However, the news has not been positively received by some Barclays shareholders.
One investor, one of the bank's 15 biggest, told Reuters that he was sceptical over the deal's value for money.
"I don't think it's an environment for banking people to be brave," he said.
"Does Barclays not have better things to do with its capital?"
The Lehman unit retains around 10,000 workers.