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.

It was the third day of hefty falls, sparked by news on Wednesday that the company admitted falsifying fuel economy data for more than 600,000 vehicles sold in Japan.
Government officials raided a company office and authorities want a full report from the company in weeks.
The shares are 40% cheaper than before news of the false data emerged.
Elsewhere on the Asian markets, shares of consumer electronics giant Sony also traded lower and closed down 1.7%.
The company trimmed nearly 10% off its previous profit estimate for the full year to March 2016, due to a one-off charge. Sony is scheduled to report its financial results next week.
On the broader Japanese market, the benchmark Nikkei 225 index reversed earlier losses and ended the Friday session higher by 1.2% - or 208.87 points - at 17,572.49.
Other Asian markets traded lower on Friday, mirroring how US markets performed overnight.
South Korea's Kospi closed down 0.33% at 2,015.49.
In Australia the S&P ASX 200 ended the week down 0.69% at 5,236.39.
China's Shanghai composite ended up 0.2% to 2,959.24.
Meanwhile in Hong Kong the Hang Seng index dropped 0.7% to trade at 21,467.
Gale force winds of up to 70mph and heavy rain will arrive in Wales on Monday evening, said the Met Office.
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Shares in Japanese automaker Mitsubishi Motors plunged 13.5% in Friday trade to close at 504 yen.