Woods and Els have agreed to skipper their sides in Melbourne, Australia, according to two people involved in the Presidents Cup.
Woods is at $11 to win at Augusta next month, alongside Jordan Spieth, Justin Thomas and Rory McIlroy, with the quartet trailing only Dustin Johnson who is the $8 favourite.
Career rivals Woods and Els famously dueled at the 2003 Cup in South Africa, when they were chosen for a play-off and were tied after three holes before the event was deemed a draw.
Els will take over the global lead reins from Zimbabwean Nick Price.
They spoke on condition of anonymity because the captain selections have not been announced, but it is expected to become official during this week's Arnold Palmer Invitational at Bay Hill.
Els and Woods could not separated, however, exchanging clutch par saves up to the fourth extra hole before darkness descended at Fancourt and the captains Jack Nicklaus and Gary Player agreed to call the first ever tied Presidents Cup. He's reached out in those team rooms and really been a big part of helping the younger players and being alongside of them and then also helping the captain with some hard tasks and asks and X's and O's. Woods had two birdies and one bogey on the day.
GETTY IMAGES Tiger Woods and Ernie Els shake hands after a match at the 2013 Presidents Cup
While Woods may have his sights set on playing in this year's Ryder Cup in France, he will serve a different role on the 2019 Presidents Cup team.
"The Presidents Cup is owned by the PGA Tour, but we have to be more in control", said Els. In gathering darkness that made it hard to read putts, Woods holed a double-breaking, 15-foot par putt on the third extra hole.
They also have battled plenty in tournaments.
It prompted four-time major victor Els, an assistant captain to Nick Price in NY, to call for sweeping changes ahead of the showpiece in Melbourne.
The Presidents Cup has found tremendous corporate support with Italian carmaker Alfa Romeo, Citibank and Rolex, but the matches lack a competitive balance. The Presidents Cup has been reduced to 30 matches over four days, and the format is not likely to change for the next one. Hale Irwin is the only playing captain in the Presidents Cup, at the inaugural matches in 1994.
South Korea praises China's role in nudging N. Korea to talks
Moon and Kim are expected to talk about a proposal for restarting communications between the North and South Korean militaries. On Saturday, Trump said his talks with Kim could end with no agreement or they could be "the greatest deal for the world".