In the book "The Handbook of Palestine and Trans-Jordan", edited by Harry Luke and Edward Keith-Roach, MMacmillan and Co., Ltd, London, 1934 (3rd Edition), the history of the establishment of Trans-Jordan is recounted.
The highlights (with my comments):
Trans-Jordan was occupied simultaneously by the British and Arab troops in October 1918.
British troops evacuated it in December 1919 - although it technically being Occupied Enemy Territory (East) and later entrusted to Britain in April 1920 at San Remo Conference - it was considered part of Syria then ruled by King Faisal.
When French troops reoccupied Syria, troops of the Britain's Royal Air Force retook it.
In August 1920, High Commissioner for Palestine travelled to Salt and announced plans for local self-government. This administration of local councils and gendarmerie proved unsuccessful.
In November 1920, Abdallah arrived from Hejaz at Ma'an. In March 1921, he proceeded to Amman.
In March 1921, in Jerusalem, Secretary for Colonies Winston Churchill arranged that Abdallah assume the administration of Trans-Jordan under the general direction of the HC for Palestine representing the Mandatory Power.
In September 1922, a Memorandum from HMG, declaring by virtue of Article 25 of the Palestine Mandate that the articles relative to the establsihment of a Jewish National Home in Palestine would be inapplicable as regards Trans-Jordan, was approved by the Council of the League of Nations.
On 25 April 1923, the HC for Palestine declared that HMG will recognize, subject to League of Nations approval, the existence of an independent Government in Trans-Jordan under the rule of Amir Abdallah. The agrrement was finally reached on 20 February 1928.
September 1923, the League of Nations finally approved the awarding of a Mandate over Palestine to Great Britain.
Prior to 12 August 1927, the HC for Palestine included in their juridiction the entire Mandatory area without separate mention of Trans-Jordan. After that date, the HCs received separate Commissions from HM as HC for Trans-Jordan.