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Dick Costolo, the former chief executive of Twitter.Credit Christian Charisius/European Pressphoto Agency

Dick Costolo, the former chief executive of Twitter, plans to leave the company’s board of directors by the end of the year or when a new chief executive is appointed, according to two people familiar with Mr. Costolo’s plans.

Mr. Costolo, who has served on Twitter’s board since September 2009, has considered stepping down from that role since he left the chief executive position in June, according to these people, who spoke on the condition of anonymity because the plans are not public.

But Mr. Costolo decided to remain on the board while Twitter searched for a full-time chief executive, these people said, to avoid adding more turbulence to a period of transition for the company. The decision to step down was Mr. Costolo’s, one of the people said.

The possibility of Mr. Costolo’s eventual exit was first reported by Bloomberg.

For months, the social media giant has faced intense scrutiny for a perceived lack of product direction and sluggish overall user growth. Investors have been eager to see the company appoint a successor as soon as possible in the hope that new leadership will boost Twitter’s growth prospects and, ultimately, its flagging stock price.

Twitter stock fell to about $27 a share on Friday, just above its initial public offering price of $26 a share in November 2013.

Jack Dorsey, a co-founder and former chief executive of Twitter, has assumed the role of interim chief executive while the company carries out a formal search for a new leader.

A Twitter spokesman declined to comment.