Richard of York was born on 21 September 1411, the son of Richard, 3rd Earl of Cambridge, by his wife Anne de Mortimer, the daughter of Roger Mortimer, 4th Earl of March. Anne Mortimer was the great-granddaughter of Lionel, Duke of Clarence, the second surviving son of King Edward III (r. 1327–1377). After the death in 1425 of Anne's childless brother Edmund, the 5th Earl of March, this ancestry supplied her son Richard, of the House of York, with a claim to the English throne that was, under English law, arguably superior to that of the reigning House of Lancaster, descended from John of Gaunt, the third son of King Edward III.
On his father's side, Richard had a claim to the throne in a direct male line of descent from his grandfather Edmund, 1st Duke of York (1341–1402), fourth surviving son of King Edward III and founder of the House of York. This made Richard a prince of blood and member of the ruling dynasty of England, which might have improved his position as contender or possible successor to the throne, even though his mother's descent already gave him a better claim anyway. His adoption of the surname "Plantagenet" in 1448 would serve to emphasize this point, namely his status as an agnate of the English royal family.
Richard's mother, Anne Mortimer, is said to have died giving birth to him, and his father, the Earl of Cambridge, was beheaded in 1415 for his part in the Southampton Plot against the Lancastrian King Henry V (r. 1413–1422). Although the Earl's title was forfeited, he was not attainted, and the four-year-old orphan Richard became his father's heir. Richard had an only sister, Isabel of Cambridge, who became Countess of Essex upon her second marriage in 1426.
Within a few months of his father's death, Richard's childless uncle, Edward of Norwich, 2nd Duke of York, was slain at the Battle of Agincourt on 25 October 1415. After some hesitation, King Henry V allowed Richard to inherit his uncle's title and (at his majority of 21) the lands of the Duchy of York. The lesser title but (in due course) greater estates of the Earldom of March also descended to him on the death of his maternal uncle Edmund Mortimer, 5th Earl of March, on 18 January 1425. The reason for Henry V's hesitation was that Edmund Mortimer had been proclaimed several times, by factions rebelling against him, to have a stronger claim to the throne than Henry's father, King Henry IV. Edmund had been a disputed heir of Richard II until his deposition by Henry IV in 1399. However, during his lifetime, Mortimer remained a faithful supporter of the House of Lancaster. Richard would inherit Edmund Mortimer's titles and claim to the throne upon his death.
Richard of York already held the Mortimer (descent from the second son of Edward III) and Cambridge (male-line descent from the fourth son of Edward III) claims to the English throne; once he inherited the March estates, as well as the Earldom of Ulster, he also became the wealthiest and most powerful noble in England, second only to the king himself. The Valor Ecclesiasticus shows that York's net income from Mortimer lands alone was £3,430 (about £350,000 today) in the year 1443–44.