"The will dated July 30th, 2001, is admitted to probate," said Superior Court Commissioner Mitchell L. Beckloff.
The step begins a process in which Smith's assets will be identified and the court will determine how they should be distributed. The will left the entirety of her estimated $710,000 in assets to her now-deceased son.
Smith also noted in the will, "I have intentionally omitted to provide for my spouse and other heirs, including future spouses and children and other descendants now living and those hereafter born or adopted."
Beckloff said he will notify Smith's mother, Virgie Arthur, of his action in case she wants to intervene legally.
But a lawyer for Stern and the estate, Bruce Ross, said he believes Arthur has no standing in the case.
The baby could inherit millions from the estate of Smith's late husband, Texas oil tycoon J. Howard Marshall II.
Outside court, Ross said he would eventually present testimony from the lawyer who drafted Smith's will, saying that Smith did not intend to disinherit Dannielynn.
"There is no provision in the will that names Dannielynn and purports to disinherit her," said the lawyer.