"Chapter 62—The Anointing of David This chapter is based on 1 Samuel 16:1-13 . A few miles south of Jerusalem, “the city of the great King,” is Bethlehem, where David, the son of Jesse, was born more than a thousand years before the infant Jesus was cradled in the manger and worshiped by the Wise Men from the East. Centuries before the advent of the Saviour, David, in the freshness of boyhood, kept watch of his flocks as they grazed on the hills surrounding Bethlehem. The simple shepherd boy sang the songs of his own composing, and the music of his harp made a sweet accompaniment to the melody of his fresh young voice. The Lord had chosen David, and was preparing him, in his solitary life with his flocks, for the work He designed to commit to his trust in after years. PP 637"
"And the Lord said unto Samuel, How long wilt thou mourn for Saul, seeing I have rejected him from reigning over Israel? fill thine horn with oil, and go, I will send thee to Jesse the Beth–lehemite: for I have provided me a king among his sons. And Samuel said, How can I go? if Saul hear it, he will kill me. And the Lord said, Take an heifer with thee, and say, I am come to sacrifice to the Lord. And call Jesse to the sacrifice, and I will shew thee what thou shalt do: and thou shalt anoint unto me him whom I name unto thee. And Samuel did that which the Lord spake, and came to Beth–lehem. And the elders of the town trembled at his coming, and said, Comest thou peaceably? And he said, Peaceably: I am come to sacrifice unto the Lord: sanctify yourselves, and come with me to the sacrifice. And he sanctified Jesse and his sons, and called them to the sacrifice. And it came to pass, when they were come, that he looked on Eliab, and said, Surely the Lord’s anointed is before him. But the Lord said unto Samuel, Look not on his countenance, or on the height of his stature; because I have refused him: for the Lord seeth not as man seeth; for man looketh on the outward appearance, but the Lord looketh on the heart. Then Jesse called Abinadab, and made him pass before Samuel. And he said, Neither hath the Lord chosen this. Then Jesse made Shammah to pass by. And he said, Neither hath the Lord chosen this. Again, Jesse made seven of his sons to pass before Samuel. And Samuel said unto Jesse, The Lord hath not chosen these. And Samuel said unto Jesse, Are here all thy children? And he said, There remaineth yet the youngest, and, behold, he keepeth the sheep. And Samuel said unto Jesse, Send and fetch him: for we will not sit down till he come hither. And he sent, and brought him in. Now he was ruddy, and withal of a beautiful countenance, and goodly to look to. And the Lord said, Arise, anoint him: for this is he. Then Samuel took the horn of oil, and anointed him in the midst of his brethren: and the Spirit of the Lord came upon David from that day forward. So Samuel rose up, and went to Ramah."
Ellen White directly references 1 Samuel 16:1-13 in this passage.