A Yahoo statement said four members will be added as part of an agreement with investment firm Starboard Value, which last month launched a bid to replace the entire Yahoo board.
"This constructive resolution will allow management and the board to keep our focus on our extremely important objectives," chief executive Marissa Mayer said in a statement.
It was not immediately clear what impact the board change would have on Yahoo's evaluation of its "strategic" options, which could involve a sale of its core Internet business.
Smith said in a statement today: "I am pleased that we were able to reach a constructive agreement with Yahoo to add new independent directors to the Yahoo board. We look forward to getting started right away and working closely with management and our fellow board members with the common goal of maximizing value for all shareholders."
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Yahoo said last week it continued to look at potential bidders and at the same time was pursuing Mayer's plan to revive growth at the company which has fallen behind rivals Google and Facebook in key areas of online advertising.
The other new board members will be Tor Braham, a former Deutsche Bank executive involved in mergers and acquisitions in the technology industry; Eddy Hartenstein, former CEO of Tribune Company, DirecTV and the Los Angeles Times Media Group; and Richard Hill, a longtime technology executive who has been chairman of Tessera Technologies since 2013.