A yellow severe weather warning has been issued as the remains of Hurricane Gonzalo reach Britain.
Coastal areas and north-western parts of Wales are expected to see the worst of the weather.
The Met Office said while all of Wales will be affected, areas including Aberporth, Aberystwyth and Anglesey will likely see the strongest winds.
"Hurricane Gonzalo will run eastwards across the Atlantic, reaching the UK on Monday night, bringing strong winds and heavy rain," said a spokesperson.
"The strongest winds are expected on Tuesday as the low pressure clears eastwards."
Gusts exceeding 55mph are likely inland, with 60 to 70mph gusts in some exposed coastal areas in the west.
The forecaster warned that fallen leaves and blocked drains could increase the risk of surface water affecting roads, and advised that travel could be disrupted.
Hurricane Gonzalo caused widespread damage and a power blackout when it hit Bermuda last week, with damage caused to houses and power lines downed.
Irish Ferries has cancelled some sailings between Holyhead and Dublin due to the adverse weather forecasts for Tuesday.
Gale force winds of up to 70mph and heavy rain will arrive in Wales on Monday evening, said the Met Office.