The move comes as public outcry against the planned payments intensified and the government opposed the awards.
Sir David – who was eligible for a bonus of up to £340,000 – said in a statement that they would be donating the money to a rail safety charity.
The former Olympic Delivery Authority chief executive said he took the decision before the row over remuneration broke out.
Higgins said: “I and my directors decided last week that we would forego any entitlement and instead allocate the money to the safety improvement fund for level crossing.
“I can confirm that remains our intention.”
Network Rail said its board “will take the opportunity to reflect further on how to incentivise performance in the company against the backdrop of the current context”.