Margaret Hodge, who chairs the Public Accounts Committee (PAC), said some justifications for the pay-offs had been "extraordinary".
Among the excessive payouts given to senior staff were £470,000 to former director-general George Entwistle after only 54 days in the job and £680,000 to former chief operating officer Caroline Thomson.
Deputy director general Mark Byford departed with a total payout of £949,000.
The committee heard evidence from outgoing HR boss Lucy Adams, current director-general Tony Hall and former director-general Mark Thompson.
Ms Hodge said: "Recent revelations over severance payments to departing senior managers have put its reputation at risk."
She said there was "a failure at the highest levels" to challenge payments to senior managers and what appears to have been a culture of cronyism that allowed for the liberal use of licence fee payers' money".
The MP also accused the BBC Trust, the corporation's governing body, of "sitting on its hands" while the pay-offs were being made.
A BBC Trust spokesman said: "Since 2009, the trust has worked successfully with the executive to drive down senior manager pay; and we support Tony Hall's speedy action to impose a cap on severance payments in the future."
Mr Thompson said in a statement: "There is absolutely no evidence of any wrongdoing by anyone at the BBC in relation to these severance payments."