Lord Blyth of Rowington, chief executive and deputy chairman of Boots, is widely tipped to take over as chairman when Lord Alexander leaves next year.
Sir David Rowland, the former chairman of Lloyd's of London who saved the insurance market from collapse, and Anthony Habgood, chief executive of Bunzl, will join the board in April. A spokesman said the move was an injection of "new blood to refresh the board".
Lord Alexander has come under attack for his stewardship of NatWest especially after last year's discovery of a pounds 90m derivatives loss at NatWest Markets, its investment banking arm, the resignation of the unit's chief executive and the sale of its equities division to Bankers Trust.
Lord Blyth has the reputation for value-driven management which analysts say would be welcomed by investors who have seen NatWest underperform its peers in the banking sector over recent years.
Lord Alexander has indicated previously that he is unlikely to continue as chairman after completing 10 years in the job in 1999.
Institutions began pressing for new board members last year after the board was seen to have made sluggish progress in fixing a merger to secure the group's long-term survival.
The bank also announced that Sir Desmond Pitcher had resigned with immediate effect. NatWest's nominations committee, which includes Derek Wanless, chief executive, had refused to renew his nomination.
Sir John Banham, who has become chairman of Tarmac and Kingfisher since joining NatWest, will stand down as he approaches the end of a five-year term.
City analysts yesterday welcomed the move. Shares rose slightly to 1168p from 1160p. As recently as last summer, the shares were languishing at around 700p.