Apple Inc. has agreed to terms with Bain Capital in the private equity firm’s 2 trillion yen ($18 billion) bid for Toshiba Corp.’s memory chip unit, paving the way for a final agreement announcement as soon as Thursday, according to people familiar with the matter.

Apple is part of a consortium of partners Bain has assembled for the offer aimed at resolving a contentious auction that has stretched over eight months, said the people, asking not to be identified because the matter isn’t public. The formal announcement may slip given Toshiba’s track record of missing deadlines, they said. Dell Inc. and SK Hynix Inc. are also providing financial support.

Apple is interested [...]