Which sentence is correct?

“Task A is complete.” or “Task A is completed.”

The word complete is both an adjective and a transitive verb.
As an adjective, complete means fully constituted of all of its parts or steps, fully carried out, or thorough.
Examples:

• The road construction is finally complete.
• Mary is planning a complete renovation of her kitchen.
• The system will reboot after the installation is complete.

As a transitive verb, complete means to bring to an end or a perfected status.
Examples:

• By 28 he completed his education and became an official, worked in different provincial courts.
• She completed her work.
• They completed the work in 3 days.

Therefore, something is complete, or something has been or was completed.

Therefore, Task A is complete (adjective), or Task A was completed (past tense verb).

Task A “is completed” is wrong, although “is being completed” or “is going to be completed” are proper verb forms.