The Expressen said Nordegren's father, Thomas Nordegren, confirmed the engagement.
'She called this morning and was incredibly happy,' Thomas Nordegren was quoted as saying. 'I only spoke shortly with them on the telephone, but they were happy and I congratulated them.'
Woods, 27, and Nordegren, 23, stayed at Shamwari Game Reserve near Port Elizabeth after the completion of last week's Presidents Cup. The Reserve was founded and is run by Adrian Gardiner, who also confirmed the news.
'I am pleased that the couple chose Shamwari for a break, and that he chose their sojourn in the wildest area of Shamwari to propose to Elin,' Gardiner said on the Shamwari Game Reserve website.
According to the website, Woods and Nordegren, who were accompanied on the trip by Woods' caddie Steve Williams and Woods' childhood friend Jerry Chang and their partners, were on a trail Tuesday and at sunset, he asked her to marry him.
There is no date or location for the wedding at this time.
Woods and Nordegren have been dating for close to two years. The couple met at the British Open where Nordegren was working as a nanny for PGA Tour player Jesper Parnevik's children.
Woods, the top-ranked player in the World Golf Rankings, finished play Sunday at the Presidents Cup. He defeated Ernie Els in their singles match, then halved three holes with Els in a playoff. After there was no more light available, the two stopped the playoff and the teams shared the Cup.