The blaze broke out on Wednesday afternoon severely damaging around a third of the structure with the main roof completely destroyed.
The Victorian pier was built in the 1870s and is home to a number of gift shops, bars and restaurants.
Osborne said: “Eastbourne Pier is a much loved local attraction and this fire is devastating news.
“I am therefore delighted to be able to provide financial support so we can minimise the effect on business and tourism.
“We will work with Eastbourne as a matter of urgency to ensure that the funding is provided without delay so people can start enjoying the pier again.”