The board strengthening comes ahead of the start of construction at its Sonora lithium project in Mexico.
A recent feasibility valued the project at US$1.25bn.
Carr is an accountant with over 25 years' experience in the resource sector on both energy and mining projects around the world.
Boyce, an accountant, was group chief financial officer Gemfields PLC, a leading supplier of gemstones that was recently acquired by Pallinghurst.
She replaces Derek Batorowski, who is stepping down as CFO to pursue other business interests but will remain a non-executive.
Peter Secker, Bacanora’s chief executive, said: “I look forward to working with both Janet and Eileen during what promises to be an exciting period for Bacanora, as we focus on embarking on the construction phase of a 35,000 tonnes per annum battery grade lithium carbonate at Sonora in H1 2018.”