Ms Wiliamson had been represented by lawyer Kamal Farouque of Maurice Blackburn.
In a statement, a spokesperson for Maurice Blackburn said: "Following ongoing discussions, Cricket Australia, Cricket Tasmania and Angela Williamson have been able to reach a mutually satisfactory resolution of the matter."
Williamson had been in the role with Cricket Tasmania for 18 months, having joined from the Department of Premier and Cabinet, when she was sacked.
In the documents lodged with the Federal Court, Ms Williamson had alleged that Cricket Tasmania had determined her role was "no longer tenable" because she had upset Health Minister Michael Ferguson and the Premier with her June 14 tweet.
Ms Williamson had taken aim at Mr Ferguson's comments in the Tasmanian Parliament, where his hesitancy to lift restrictions on abortions in public hospitals was, according to Ms Williamson, "irresponsible, gutless and reckless".