Chelsea's Women's Super League title defence will begin against Manchester City, while Manchester United's first senior competitive women's game since 2005 will be at Liverpool in August.
The fixtures for the new, full-time WSL - which begins on the weekend of 8-9 September - were released on Wednesday.
Second-tier newcomers United are in Liverpool's Continental Tyres League Cup group, starting from 18-19 August.
This summer, the Football Association revamped England's top women's leagues.
The WSL, which will contain 11 professional teams for the first time, sees a meeting of last season's top two - Chelsea and Man City - at Kingsmeadow on the opening weekend.
Arsenal's campaign will begin at home to Liverpool, now managed by former Leeds United men's boss Neil Redfearn, while top-flight newcomers Brighton will host Bristol City.
Elsewhere, Birmingham City will host Everton, while Yeovil Town will travel to Reading, with newly-promoted West Ham United sitting out the first round of fixtures owing to the league containing an odd number of teams.
The League Cup sees the 22 tier one and tier-two clubs split in to four groups, with the top two teams from each group progressing to 8-9 January's quarter-finals.
New teams, new names, new licence criteria
The FA, which runs the women's leagues in England, restructured the top divisions this summer after an application process for licences for tiers one and two, with all top-flight clubs training full-time in 2018-19.
West Ham have moved up to the WSL from the third tier, while Brighton have moved up from the old WSL 2.
In the part-time, second-tier now known as the Championship, Manchester United are among six new sides.
Charlton, Leicester City, Lewes FC and Sheffield United joined the Red Devils in earning licences in May, before Crystal Palace were also added after Doncaster Rovers Belles and Sheffield FC both withdrew from the second tier.
- Full Women's Super League fixtures
- Full Women's Championship fixtures
- Women's Continental Tyres League Cup fixtures
New, one-off rules on promotion & relegation
With those changes leaving 11 sides in each of the top two leagues, the FA also confirmed on Wednesday their adjusted arrangements for promotion and relegation.
From the top flight, one side will be relegated at the end of 2018-19.
The top two sides in the Championship will be eligible to win promotion up to the WSL - provided they can meet the professional criteria for a licence next summer.
There will no relegation from the bottom of the Championship, down to the third tier - the regionalised FA Women's National League.
And, for one season only, up to two sides could win promotion from tier three to the Championship next summer - with both the Northern and Southern winners initially eligible, rather than just the winners of a play-off between the two.
That is with view to seeing 12 teams in each of the top two divisions by 2019-20.
If the winner of either the Northern or Southern sections are unable to meet criteria for promotion then the respective runner-up in that division will be offered the opportunity to apply to go up instead.
The FA then hope to implement a consistent one-up, one-down system between the top three tiers from the 2019-20 campaign onwards.