But he only paid about two years' worth of instalments before the relationship ended.
Stark claimed he was in breach of his vow and a later agreement in which he pledged £200,000 to secure a home for her.
But Mr Walker, 60, insisted he owed nothing and the agreements were not legally binding.
Ruling against Stark, Judge David Halpern QC said she had been "living beyond her means for many years".
He said Mr Walker had intended the letter to appear legally binding to ensure continued access to their child.
Judge Halpern added: "He did so by using formal language and by including a reference to the term ‘guarantee' (which was meaningless in this context), but he was careful to add the words ‘love and kindness' in order to ensure it would not stand up in a court of law.
He intended it to be nothing more than a ‘gentlemen's agreement'.
I am not satisfied on the balance of probabilities that the opportunity to write a column for The Times was revived in 1997, nor that it was turned down in consideration of Mr Walker agreeing to pay her the sums set out in the letter."
Stark dated the Duke of York from 1982 to 1983. They were tipped to marry but split amid media pressure and Palace concern over topless images and her naked lesbian romp in film Emily.
Prince Andrew's controversial ex Koo Stark has lost a legal battle with a former partner she claimed promised her £50,000 a year for life.
The US actress, 63, said Warren "Robbie" Walker made the vow in a 1997 letter after they had a child together.
But the financier branded her a "gold-digger" in evidence to the High Court – where a judge has now ruled his note was just a "gentlemen's agreement".
Stark claimed he made the cash offer in return for her giving up plans to write a column called Diary of a Single Mother for The Times, as publicity-shy Mr Walker thought the idea "distasteful and unethical".
The letter said he would "guarantee" the "equivalent of £50,000" a year out of "kindness and love".