This wiki entry is created in response to a few forum threads (links at bottom) asking for this method. Feel free to contribute to this article with explanations or code.

Drag and Drop within a GridView

This example will demonstrate the iOS style (video here ) of dragging and dropping ListModel elements within a GridView.

There are three files in this example. One for the model (WidgetModel.qml), one for the delegate (IconItem.qml) and one for the GridView (Main.qml).

WidgetModel.qml

import QtQuick 1.0
ListModel {
ListElement { icon: "Images/widget1.png"; gridId: 0}
ListElement { icon: "Images/widget2.png"; gridId: 1}
ListElement { icon: "Images/widget3.png"; gridId: 2}
ListElement { icon: "Images/widget4.png"; gridId: 3}
ListElement { icon: "Images/widget5.png"; gridId: 4}
ListElement { icon: "Images/widget6.png"; gridId: 5}
ListElement { icon: "Images/widget7.png"; gridId: 6}
ListElement { icon: "Images/widget8.png"; gridId: 7}
ListElement { icon: "Images/widget9.png"; gridId: 8}
}

IconItem.qml

import QtQuick 2.0

Component {
    Item {
    id: main
    width: grid.cellWidth; height: grid.cellHeight

    Image {
        id: item; parent: loc
        x: main.x + 5; y: main.y + 5
        width: main.width - 10; height: main.height - 10;
        fillMode: Image.PreserveAspectFit; smooth: true
        source: icon

        Rectangle {
            anchors.fill: parent;
            border.color: "#326487"; border.width: 6
            color: "transparent"; radius: 5
            visible: item.state = "active"
        }

        Behavior on x {
            enabled: item.state != "active"
            NumberAnimation { duration: 400; easing.type: Easing.OutBack }
        }

        Behavior on y {
            enabled: item.state != "active"
            NumberAnimation { duration: 400; easing.type: Easing.OutBack }
        }

        SequentialAnimation on rotation {
            NumberAnimation { to:  2; duration: 60 }
            NumberAnimation { to: -2; duration: 120 }
            NumberAnimation { to:  0; duration: 60 }
            running: loc.currentId !== -1 && item.state !== "active"
            loops: Animation.Infinite; alwaysRunToEnd: true
        }

        states: State {
            name: "active"; when: loc.currentId === gridId
            PropertyChanges { target: item; x: loc.mouseX - width/2; y: loc.mouseY - height/2; scale: 0.5; z: 10 }
        }

        transitions: Transition { NumberAnimation { property: "scale"; duration: 200} }
        } //Image
    } //Item
} //Component

Main.qml

import QtQuick 2.0
import QtQuick.Controls 2.2

ApplicationWindow {
    width: 640; height: 480
    color: "#222222"
    visible: true

    GridView {
        id: grid
        interactive: false
        anchors.fill: parent
        topMargin: 60
        bottomMargin: 60
        leftMargin: 140
        rightMargin: 140

        cellWidth: 120
        cellHeight: 120
        model: WidgetModel { id: icons }
        delegate: IconItem { }
    }

    MouseArea {
        property int currentId: -1 // Original position in model
        property int newIndex // Current Position in model
        property int index: grid.indexAt(mouseX, mouseY) // Item underneath cursor

        id: loc
        anchors.fill: parent
        onPressAndHold: currentId = icons.get(newIndex = index).gridId
        onReleased: currentId = -1
        onPositionChanged: {
            if (currentId !== -1 && index !== -1 && index !== newIndex)
                icons.move(newIndex, newIndex = index, 1)
        }
    }
}

Video

Relevant forum threads:
iOS Style Rearrange of Icons