According to the Watchtower Society's Publications, Elders are Appointed directly by the Governing Body of Jehovah's Witnesses, or by Overseers who have been directly Appointed by the Governing Body. The Watchtower Society teaches that Elders are direct Representatives of the Governing Body:

Quotes from "The Watchtower", January 15, 2001 Issue, Pages 14-15:

The Governing Body of Jehovah's Witnesses directly appoints all members of Branch Committees. When deciding who can assume such a weighty responsibility, the Governing Body has in mind Jesus' statement: "Everyone to whom much was given, much will be demanded of him; and the one whom people put in charge of much, they will demand more than usual of him." (Luke 12:48) In addition to appointing Branch Committee members, the Governing Body appoints Bethel elders and traveling overseers. However, they do commission responsible brothers to act for them in making certain other appointments.

[...] Today, therefore, the Governing Body appoints qualified brothers at the branches to represent it in making appointments of elders and ministerial servants. Care is taken that those acting representatively on behalf of the Governing Body clearly understand and follow the Scriptural guidelines for making such appointments. Hence, it is under the direction of the Governing Body that qualified men are appointed to serve in the congregations of Jehovah's Witnesses worldwide.

When recommendations for appointment of overseers and ministerial servants are submitted to a branch office of the Watch Tower Society, experienced men rely on God's spirit for gui dan ce in making the appointments. These men feel a sense of accountability, realizing that they must not lay their hands hastily upon any man, lest they share in his sins.-1 Timothy 5:22.

Certain appointments may be transmitted by a letter bearing an official stamp from a legal entity. Such a letter may be used to appoint more than one brother in the congregation.

Theocratic appointments come from Jehovah through his Son and God's visible earthly channel, "the faithful and discreet slave" and its Governing Body. ( Matthew 24:45-47) The whole process of such recommendation and appointment is directed, or guided, by holy spirit.

Quote from "The Watchtower", January 15, 1996 Issue, Page 15:

Today, Christian elders are appointed by the Governing Body of Jehovah's Witnesses

Quote from "The Watchtower", July 1, 1994 Issue, Page 22:

the Governing Body delegates authority to Branch Committees, district and circuit overseers, and elders within each of the more than 73,000 congregations of Jehovah's Witnesses throughout the earth. All these devoted Christian men deserve our support and respect.

Quote from "The Watchtower", February 1, 1993 Issue, Page 16:

The facts show that today "the faithful and discreet slave" is associated with Jehovah's Witnesses and represented by the Governing Body of these Witnesses. That body, in turn, appoints overseers in various capacities-such as elders and traveling representatives-to direct the work on a local level. Godly subjection requires each dedicated Witness to be in subjection to these overseers in keeping with Hebrews 13:17: "Be obedient to those who are taking the lead among you and be submissive, for they are keeping watch over your souls as those who will render an account; that they may do this with joy and not with sighing, for this would be damaging to you."

Quote from "The Watchtower", June 1, 1992 Issue, Page 18:

Those taking the lead in the congregation are the elders. True, these men are not perfect. Nevertheless, they are appointed under the supervision of the Governing Body.

Quote from "The Watchtower, July 1, 1992 Issue, Page 14:

AS SUPREME Judge, Jehovah has delegated judicial authority to his Son. (John 5:27) In turn, as Head of the Christian congregation, Christ uses the faithful and discreet slave class and its Governing Body to appoint elders, who at times have to act as judges. ( Matthew 24:45-47; 1 Corinthians 5:12, 13; Titus 1:5, 9)

Quote from "The Watchtower", November 15, 1991 Issue, Pages 19-20:

Elders are appointed by the Governing Body of Jehovah's Witnesses or its direct representatives. That body, in turn, represents "the faithful and discreet slave."

Quote from "The Watchtower", March 15, 1990 Issue, Page 20:

21 Under the direction of the holy spirit, Branch Committees recommend mature, spiritual men to serve as circuit and district overseers. After being appointed directly by the Governing Body, they serve as traveling overseers. These brothers visit circuits and congregations in order to build them up spiritually and help them apply instructions received from the Governing Body. (Compare Acts 16:4; Romans 1:11, 12.) Traveling overseers submit reports to the branch office. With the help of the holy spirit and the inspired Scriptures, they share with local elders in recommending qualified brothers for appointment as ministerial servants and elders by the Governing Body or by its representatives.-Philippians 1:1; Titus 1:5; compare 1 Timothy 3:1-13; 4:14.22 In turn, those making up bodies of elders 'pay attention to themselves and to all the flock, among which the holy spirit has appointed them overseers.' (Acts 20:28 ) These overseers faithfully seek to apply instructions received from Jehovah God and Jesus Christ by means of the faithful and discreet slave and its Governing Body.

End of Quotes about Elders being Appointed by the Governing Body