The veteran politician died last week aged 84 following a short illness.
His family said in a statement that he wanted his body to be left to Edinburgh University for research, followed by a private interment.
A memorial service will be held at St Michael’s Parish Church in Linlithgow on Friday February 24 at 1pm.
A further service will be held in London at a date yet to be announced.
Mr Dalyell spent 43 years as an MP after being elected to represent West Lothian in 1962.
The Old Etonian baronet became MP for Linlithgow 21 years later and was named Father of the House - the longest continuously serving MP - in 2001.
Tributes were paid to him from across the political spectrum after his death was announced on January 26.
Labour leader Jeremy Corbyn called him a ‘’titan of parliamentary scrutiny’’, while Scottish First Minister Nicola Sturgeon said he was a ‘’real giant’’ of Scottish politics.