She will take over from Amanda Jupp, while Lionel Barnard will serve as her deputy chairman.
Mrs Arculus is a former cabinet member and select committee chairman. Previously she worked in IT, as an office manager and has also been actively involved in voluntary work.
She is a vice-president of Arundel and South Downs Conservative Association having held the post of treasurer twice.
She is married with two grown-up children and two grandchildren and has lived in West Sussex for 39 years.
She said: “It will be a privilege to take forward the role from Amanda who has done a wonderful job with Nigel.
“I’m looking forward to representing West Sussex enormously. I love this beautiful part of the country and I see the role of chairman, together with Lionel my vice-chairman, very much as helping to enhance this great county.
“I can’t wait to get started.”
The chairman presides over meetings of the council and ensures the council acts in the best interests of all the residents of the county.
Both chairman and vice-chairman also serve as the civic head representing the authority inside and outside West Sussex.
Cllr Barnard is a former cabinet member and deputy leader, lastly holding the portfolio for residents’ services, is a published author and was formerly a bookseller.
He was chairman of Henfield Conservatives from 1996 to 2000 and was re-elected for 2008 to 2009.
Married with one son, his hobbies are politics and current affairs, reading American crime novels and astronomy.
He said: “It is a great honour to serve West Sussex in this capacity and to support Pat in everything that she does. Pat and I were first elected in 2001 and have worked together since then. I would like to pay tribute to both Amanda and Nigel, who have done a splendid job. Both will be a hard act to follow.”
Mrs Jupp and outgoing vice-chairman Nigel Peters have attended hundreds of events across the county over the past two years, including hosting a reception in July, 2014, to celebrate the 125th anniversary of the council.
She said: “It has been a great privilege and honour to serve as chairman of WSCC and I have thoroughly enjoyed the last two years.
“It has enabled me not only to have an extraordinary insight into the myriad workings of the council but also to experience the enormous contribution made by other groups and organisations, not least that of the voluntary sector.
“I have also been most fortunate to have had the tireless support of Nigel Peters as vice-chairman as well as the opportunity to work more closely with colleagues.”