'cross over the river' is correct and can be used in written English.
You could use this phrase when talking about someone travelling or moving from one side of a river to another. For example, "The hikers decided to cross over the river in order to reach the next campsite."
"Let us cross over the river and rest in the shade of the trees".
Walk down Garret Hostel Lane from Trinity Lane in the centre of Cambridge, cross over the river and cross Queen Street at the lights.
Pass the infantry to the front!" Jackson died at 3 15 p.m. His final words: "Let us cross over the river and rest under the shade of the trees".
Cross over the river once more on Hampton Court Bridge and Hampton Court station, with its regular trains back to Richmond or London's Waterloo, is right in front of you.
From the pulpit, Obama paid tribute to "the Moses generation" — to Martin Luther King and John Lewis, to Anna Cooper and the Reverend Joseph Lowery — the men and women of the movement, who marched and suffered but who, in many cases, "didn't cross over the river to see the Promised Land".
When he and Mrs. Jackson told the stricken general that he was going to die, he calmly replied that he hoped it would be on "the Lord's day," and his last words were "Let us cross over the river and rest under the trees".
As the train crossed over the Chicago river, my girls had their hands pressed up against the windows, looking at all the skyscrapers illuminated red and green.
Starting at the exquisite Tintern Abbey, the walk heads along the western bank of the River Wye before crossing over the river and uphill on wooded paths towards ancient Offa's Dyke.
The state highway leaves the steel complex by crossing over the Patapsco & Back Rivers Railroad and Wharf Road, also identified as MD 151B, with which MD 151 has a modified trumpet interchange.
