The golfer's agent, Mark Steinberg of IMG, confirmed the couple's engagement to Associated Press on Friday but declined to give details.
"She called this morning and was incredibly happy," Nordegren's father, Thomas, told the Swedish newspaper Expressen. "I only spoke shortly with them on the telephone, but they were happy and I congratulated them."
Thomas Nordegren, a correspondent for Swedish Radio in Washington, could not immediately be reached for comment by AP.
Ashley Cocks, a spokesman for the Shamwari Game Reserve in South Africa, said in a statement that Woods proposed to Nordegren while they were at the game park outside Port Elizabeth. Woods had been in Fancourt, South Africa, for the Presidents Cup, which ended Sunday.
The proposal came during a walk at sunset Tuesday, Cocks said, adding that when the couple left Friday aboard a private jet, Nordegren had a "huge diamond on her finger."
Nordegren's mother, Barbro Holmberg, who is Sweden's migration minister, had no comment.
Woods, 27, and Nordegren, a 23-year-old model, have been dating for nearly two years.
The South African Broadcasting Corp. also reported the engagement.